WM7A 


LIBRARY 

UNIVERSITY  OF  CALIFORNIA 
DAVIS 


Digitized  by  the  Internet  Archive 

in  2007  with  funding  from 

IVIicrosoft  Corporation 


http://www.archive.org/details/energychangesinvOOrichrich 


Energy  Changes  Involved  in  the  Dilution 
of  Zinc  and  Cadmium  Amalgams 


BY 


THEODORE  WILLIAM  RICHARDS 

AND 

GEORGE  SHANNON  FORBES 
Of  Harvard  University 


WASHINGTON    D.  C: 

Published  by  the  Carnegie  Institution  of  Washington 
1906 


LIBRARY 


Carnegie  Institution  of  Washington, 
Publication  No.  56 


contributions  from  the  chemical  laboratory 
OF  harvard  college 


THE  FRIKDENWALD  COMPAKY 
BALTIMOKR,   MU.,  V.  H.  A. 


TABLE  OF  CONTENTS 

PAGE. 

Introduction    i 

The  Aim  and  Scope  of  the  Present  Research 8 

The  Values  of  the  Constants 9 

The  Density  of  Amalgams   11 

The  Purity  of  the  Materials   15 

Precautions  Used  in  the  Preparation  of  Amalgams 17 

The  Cell  and  Its  Manipulation 21 

The  Potentiometer  and  Its  Calibration  23 

The  Standard  of  Potential 28 

The  Electromotive  Force  between  Zinc  Amalgams 30 

Influence  of  the  Concentration  of  the  Electrolyte 44 

The  Electromotive  Force  between  Cadmium  Amalgams  46 

The  Temperature  Coefficient  of  Amalgam  Cells 49 

The  Measurement  of  the  Heat  of  Dilution  of  the  Amalgams 51 

The  Application  of  the  Equation  of  Helmholtz 57 

The  Application  of  the  Formula  of  Cady 58 

The  Probable  Causes  of  the  Deviations 59 

The  Application  of  the  Gas  Law  at  Infinite  Dilution 65 

Summary    68 


ILLUSTRATIONS 


PAGE, 

Fig.  I.    The  Densities  of  Zinc  and  Cadmium  Amalgams 14 

2.  Device  for  Preserving  Amalgams 19 

3.  A  Rack  with  Pipettes 20 

4.  Amalgams  in  Cell  ready  for  Potential  Measurement 22 

5.  The  Potentiometer   24 

6.  The  Preliminary  Results  with  Zinc  Amalgams 36 

7.  The  Final  Results  with  Zinc  Amalgams  free  from  Oxidation 45 

8.  The  Results  with  Cadmium  Amalgams 49 

9.  The  Apparatus  for  Measuring  Heat  of  Dilution 53 

10.    The  Approach  to  the  Gas  Law  at  Infinite  Dilution 66 

iii 


ENERGY   CHANGES   INVOLVED   IN  THE   DILUTION   OF 
ZINC   AND   CADMIUM  AMALGAMS. 


By  Theodore  William  Richards  and  George  Shannon  Forbes. 


INTRODUCTION. 

Nearly  half  a  century  ago  a  French  physicist  named  Gaugain  published  a 
note  ^  on  his  investigation  of  a  voltaic  pile  whose  "  negative  metal "  was 
a  dilute  amalgam  of  zinc  or  cadmium.  At  first  the  electromotive  force  rose 
very  rapidly  when  the  proportion  of  oxidizable  metal  was  increased,  but 
beyond  a  certain  point  the  introduction  of  fresh  quantities  of  zinc  caused  no 
further  variation.  He  concluded  that  these  phenomena  were  occasioned  by 
the  affinity  of  the  mercury  for  the  amalgamated  metal,  an  affinity  which 
varied  with  the  proportions  of  the  amalgam.  He  also  found  that  cadmium 
always  had  an  electromotive  force  greater  than  its  amalgams,  no  matter 
whether  these  contained  cadmium  in  mere  traces  or  in  sufficient  quantities 
to  form  a  solid  compound. 

Shortly  after,  M.  E.  Becquerel  *  published  an  exhaustive  and  scholarly 
treatise  on  the  "  Disengagement  of  electricity  in  voltaic  piles."  His  experi- 
mental skill  and  his  logical  interpretation  of  results  appear  remarkable  when 
we  consider  the  limitations  of  exact  knowledge  at  that  time.  In  this  paper 
he  suggested  the  probable  existence  of  an  approximate  relation  between 
the  heats  of  combustion  of  diflferent  metals  and  their  electromotive  forces, 
and  pointed  out  the  importance  of  further  work  in  this  direction.  Among 
the  many  substances  examined  by  him  were  amalgams  of  zinc,  manganese, 
ammonium,  barium,  calcium,  sodium,  and  potassium.  The  dependence  of 
electromotive  force  upon  concentration  was  noted  over  a  wide  range,  but  no 
attempt  was  made  to  explain  it.  Very  little  improvement  in  the  experi- 
mental or  theoretical  treatment  of  amalgams  was  made  for  thirty  years 
after  the  publication  of  this  work. 

In  1863  Crova '  concluded  that  amalgams  containing  from  i  to  5  per  cent 
of  zinc  could  be  substituted  for  the  zinc  in  a  Daniell  cell  without  change  of 


^  Comptes  Rendus,  42,  430  (1856). 
'Ann.  Chem.  Phys.,  48,  266  (1856). 
'Ibid.,  68,  458  (1863). 


ENERGY   CHANGES  INVOLVED   IN   DILUTION   OF  AMALGAMS. 


electromotive  force.  When  the  proportion  of  zinc  was  reduced  to  four- 
tenths  of  I  per  cent  the  electromotive  force  sank  to  nine-tenths  of  its  orig- 
inal value.  It  is  interesting  to  note  that  he  considered  the  phenomena 
observed  by  Gaugain  as  quite  analogous  to  the  decrease  of  electromotive 
force  in  a  cell,  due  to  polarization. 

In  1879  Hockin  and  Taylor  *  made  extended  observations  on  the  electrical 
behavior  of  solid  and  liquid  amalgams.  Unfortunately  their  original  paper 
is  inaccessible.  Their  work,  however,  does  not  seem  to  have  extended  appre- 
ciably the  theoretical  knowledge  of  these  concentration  effects. 

Three  years  later  Helmholtz "  published  his  masterly  paper  on  the  "  Gal- 
vanic current  caused  by  differences  in  concentration."  The  relation  between 
the  vapor  tensions  over  two  different  aqueous  solutions  of  a  given  electrolyte 
was  made  the  basis  for  the  calculation  of  the  electromotive  force  between 
them.  It  was  also  pointed  out  that  the  latter  should  vary  as  the  absolute 
temperature.  Measurements  on  cells  of  copper  sulphate  and  of  zinc  sul- 
phate were  in  good  agreement  with  the  predicted  values. 

Elements  consisting  of  concentrated  amalgam  as  one  electrode,  and  dilute 
amalgam  as  the  other,  with  an  interposed  solution  of  metallic  salt,  although 
analogous  to  aqueous  concentration  cells,  appear  to  have  been  altogether 
disregarded  up  to  this  time,  and,  in  fact,  for  eight  years  after  it.  Gaugain, 
Becquerel,  and  the  others  had  all  aimed  to  improve  the  galvanic  cell  as  a 
practical  source  of  electricity.  So  when  they  attempted  to  explain  the 
peculiar  behavior  of  amalgams  they  always  considered  these  separately  in 
their  relation  to  copper,  platinum,  zinc,  or  pure  mercury,  and  never  in 
relation  to  each  other.  Naturally  little  progress  could  be  made  by  such 
considerations. 

In  1888  Lindeck  determined  the  potential  of  various  amalgams  of  zinc, 
cadmium,  lead,  tin,  and  silver  against  amalgamated  zinc  in  zinc  sulphate  solu' 
tion.  His  measurements  on  zinc  and  silver  amalgams  are  the  most  im- 
portant.    A  part  of  them  are  given  below. 

(2)    Silver  amalgams. 


( I )     Zinc  amalgams . 

Per  cent  of 
zino. 

E.  M.  F. 

Per  cent  of 
zinc. 

B.  M.  F. 

1.860 
0.467 
0.064 
0.028 
0.0014 

0.003 
0.022 
0.047 
0.057 
0.096 

0.0010 

0.00038 

0.00027 

0.00020 

0.00015 

0.11 
0.13 
0.14 
0.15 
0.16 

Per  cent  of 
silver. 

E.  M.  F. 

Saturated. 
2.0 
0.57 

1.32 
1.30 
1.33 

*  Journ.  Soc.  Tal.,  8,  282  (1879).    "  The  Voltaic  Cell,"  by  Park  Benjamin,  pp.  148-151. 
°  Abstract,  Chem.  Cent.  Blatt,  [3]  13,  648  (1882). 


HISTORICAL   INTRODUCTION.  3 

It  may  be  remarked  in  passing  that  the  difference  between  any  two  electro- 
motive forces  in  the  first  table  would  give  at  once  the  potential  of  a  con- 
centration cell  containing  the  two  corresponding  amalgams. 

In  his  theoretical  discussion  Lindeck  calls  attention  to  the  fact  that  the 
metal  silver  behaves  like  mercury  from  an  electrochemical  standpoint. 

The  following  year  Ramsay '  determined  the  molecular  weights  of  almost 
all  known  metals  by  measurement  of  the  vapor  tension  of  mercury  over 
their  amalgams.  In  general  the  results  were  in  agreement  with  the  accepted 
atomic  weights  of  the  various  metals.  Sodium  and  calcium,  however,  ap- 
peared unmistakably  smaller,  suggesting  the  subdivision  of  their  atoms,  and 
causing  anxiety  among  some  upholders  of  the  atomic  theory. 

In  this  same  year  Nernst  published  his  well-known  fundamental  paper  on 
"  Die  Electromotorische  Wirksamkeit  der  lonen."  This  paper  did  not  dwell 
upon  amalgam  cells  in  particular,^  but  its  application  thereto  is  manifest. 

In  April,  1890,  von  Tiirin "  published  a  complete  theory  of  amalgam  con- 
centration cells,  as  a  possible  means  of  determining  the  molecular  weights 
of  the  metals.     He  first  considered  a  cell  of  the  type 

Mercury,  Mercuric  salt,  Amalgam  of  "noble"  metal. 

Applying  the  osmotic  theory  developed  three  years  before  by  van't  Hoff,' 
he  concluded  that  the  electromotive  force  E  was  given  by  the  equation 

E  =  1.728  X  10-*  (^)  —  when  T  is  the  absolute  temperature  and  -??-the 

number  of  kilogram  molecules  of  the  metal  in  a  cubic  meter  of  mercury. 
The  cell  of  the  type 

Zinc  amalgam  concentrated.  Zinc  sulphate,  Zinc  amalgam  dilute, 

required  different  mathematical  treatment.  Pointing  out  the  analogy  be- 
tween such  an  element  and  the  cells  investigated  by  Helmholtz,  he  decided 
that 

E  =  9.s636X  10' Tqk  log  ^ 

where  q  is  the  electrochemical  equivalent  for  zinc,  k  the  ratio  between  the 

molecular  weights  of  mercury  and  zinc,  and   -^  the  concentration  ratio  of 

the  amalgams.  The  paper,  while  very  able,  is  somewhat  marred  by  various 
minor  errors,  and  contains  no  experimental  data  to  support  the  formulae 


"Journ.  Chem.  Soc,  55,  521  (1889). 
'Zeit.  Phys.  Chem.,  4,  129   (1889). 
'Zeit.  Phys.  Chem.,  5,340  (1890). 
•Zeit.  Phys.  Chem.,  1,  481  (1887). 


4  ENERGY   CHANGES  INVOLVED   IN   DILUTION   OF  AMALGAMS. 

deduced.  It  clearly  establishes  the  priority  of  von  Tiirin  in  announcing  a 
consistent  theory  for  amalgam  cells,  although  it  is  probable  that  G.  Meyer 
had  already  worked  out  much  of  it  independently. 

In  May,  1890,  Meyer  "  published  a  research  on  "  The  electromotive  forces 
between  glass  and  amalgams."  Working  at  high  temperatures  the  glass 
behaved  as  an  electrolyte,  and  he  was  able  to  measure  cells  of  the  type 

Mercury,  Glass,  Sodium  amalgam. 
By  subtraction  of  the  potentials  of  two  cells  containing  amalgams  of  differ- 
ent concentrations,  he  calculated  the  potential  of  several  cells  of  the  type 

Sodium  amalgam  dilute,  Glass,  Sodium  amalgam  concentrated. 
He  showed  the  process  taking  place  in  such  an  element  to  be  reversible,  and 
pointed  out  that  the  electromotive  force  should  be  proportional  to  the  abso- 
lute temperature  in  case  the  heat  of  dilution  was  negligible.  But  his  attempt 
to  apply  the  principles  laid  down  by  Helmholtz  was  incomplete,  and,  so  far 
as  it  went,  discordant  with  his  results.  In  a  postscript  to  this  article,  how- 
ever, he  mentioned  the  article  of  von  Turin,  and  stated  that  he  had  been  for 
two  months  past  occupied  in  determining  the  molecular  weights  of  zinc  and 
cadmium  in  mercury  by  a  very  similar  method.  These  both  corresponded 
with  their  atomic  weights,  and  further  investigation  was  in  progress. 

In  November  of  the  same  year,  von  Tiirin,"  in  an  address  before  the  Rus- 
sian Physico-Chemical  Society,  proved  that  his  theoretical  conclusions  were 
verified  by  the  measurements  of  Lindeck.  He  showed  that  all  the  metals 
investigated  in  that  research  were  monatomic,  and  pointed  out  the  bearing 
of  Ramsay's  experiments"  upon  the  question  at  issue.  No  review  of  this 
address  appeared  in  any  German  periodical  at  the  time.  In  February,  1891, 
von  Tiirin  "  corrected  and  amplified  his  first  paper,  but  said  nothing  about 
the  work  of  Lindeck. 

Three  months  later  G.  Meyer  "  published  his  well-known  research  on  the 
"  Molecular  weights  of  some  metals,"  and  reiterated  his  claim  to  priority  in 
confirming  the  theoretical  formula  by  experiment.  He  then  developed  the 
equation  for  zinc  amalgam  cells  from  a  consideration  of  the  osmotic  work 
involved  in  a  reversible  cycle — a  more  direct  treatment  than  von  Tiirin's. 

In  the  formula  E  =  1.908   ^   T  log  ^  ,  ^  represents  the  electrochemical 

equivalent,  in  grams,  of  the  metal,  and  m  the  molecular  weight  of  the  metal 

"Wied.  Ann.,  40,  244  (1890). 
"Zeit.  Phys.  Chem.,  8,  141   (1891). 
"J.  Chem.  Soc.,  55,  521   (1889). 
"Zeit.  Phys.  Chem.,  7,  221   (1891). 
''Ibid.,  477  (1891). 


HISTORICAL  INTRODUCTION.  5 

in  the  amalgam.  The  electromotive  force  between  dilute  amalgams  of  zinc, 
cadmium,  lead,  tin,  copper,  and  sodium  were  measured  with  a  fair  degree 
of  accuracy.  The  conclusion  that  these  metals,  including  sodium,  were 
monatomic  in  mercurial  solution  appeared  well  founded.  Referring  to  Ram- 
say's work  on  sodium,  he  speaks  of  his  own  failure  to  confirm  it  at  the  low 
temperature  prevailing  in  his  research. 

Von  Tiirin,"  in  commenting  upon  Meyer's  paper,  called  attention  to  his 
address  before  the  Russian  Society,  but  he  still  failed  to  mention  Meyer's 
preliminary  announcement  in  Wiedemann's  Annalen. 

His  oversight  in  this  respect  may  account  for  his  ill-founded  claim  to 
precedence  in  the  experimental  as  well  as  the  theoretical  development  of  the 
subject. 

The  relation  of  the  special  equations  of  von  Tiirin  and  Meyer  to  the  general 

equation  of  Nernst,  E—  —^  In  ~ ,  is  sufficiently  evident  without  further 

comment. 

Seven  years  of  inactivity  in  this  line  of  investigation  followed,  and  the 
reason  for  the  discrepancy  between  Meyer's  and  Ramsay's  results  on  sodium 
were  still  unexplained. 

In  1898  Schoellers"  prepared  various  amalgams  of  sodium  and  barium 
electrolytically,  compared  them  with  normal  electrodes,  and  determined  their 
concentration  analytically.  From  a  pair  of  such  measurements,  on  either 
metal,  the  electromotive  force  of  the  corresponding  amalgam  cell  could  be 
found  by  subtraction.  This  in  each  case  agreed  well  with  the  potential  de- 
manded by  the  logarithmic  formula,  on  the  assumption  sodium  and  barium 
were  monatomic.  This  research,  however,  was  crude  and  left  the  question 
at  issue  still  unsettled. 

In  October,  1898,  Richards  and  Lewis  presented  to  the  American  Academy 
their  research  on  zinc  and  cadmium  amalgams.  Accurate  determinations  of 
electromotive  force  showed  that  zinc  amalgams  so  concentrated  as  i  per 
cent,  and  cadmium  amalgams  of  3  per  cent  obeyed  the  laws  of  dilute  solu- 
tions with  considerable  fidelity.  Neither  the  concentration  of  the  electro- 
lyte nor  the  nature  of  its  anion  had  any  influence  upon  the  results,  and  the 
potentials  were  strictly  proportional  to  absolute  temperature.  The  second 
and  third  of  these  points,  though  inferred  from  the  derivation  of  the  formula, 
had  not  previously  been  verified  by  experiment.     More  important  still  was 


"Zeit.  Phys.  Chem.,  8,  141  (1891). 

"Chem.  Cent.  Blatt,  70,  I,  16  (1899);  Zeitschr.  Electrochem.,  5,  259  (1899). 


O  ENERGY   CHANGES   INVOLVED   IN   DILUTION   OF  AMALGAMS. 

a  calculation  of  h,  the  heats  of  amalgamation  of  zinc  and  cadmium,  from 
the  temperature  coefficient  of  cells  of  the  type 

Electrolytic  zinc,  Zinc  sulphate,  Zinc  amalgam. 

If  the  equation  of  Helmholtz  is  thrown  into  the  form  E  =  T^^  +  h, 

a  J 

h  can  be  found  by  assuming  that  ~j^^  and  h  are  nearly  constant  at  all  tem- 

peratures.  The  result  for  zinc  agreed  so  well  with  Favre's"  calorimetric 
determination  that  confidence  was  placed  in  the  value  proposed  for  cadmium. 
Another  significant  paper  was  published  by  Cady"  in  December  of  the 
same  year.  Working  with  sodium  and  calcium  amalgams  (the  former  more 
concentrated  than  Meyer's),  he  obtained  molecular  weights  for  the  two 
metals  in  striking  agreement  with  Ramsay's  results.  He  now  measured  Q, 
the  heat  of  dilution  of  sodium  amalgam,  and  found  that  its  conversion  into 
electrical  energy  would  account  for  the  abnormally  high  potential  of  the 
corresponding  cell.  In  other  words,  Meyer's  expression  must  be  replaced, 
in  such  a  case,  by  the  formula 

^>EF=Q^  RT  In  ^. 

Ramsay's  value  for  sodium  could  be  made  normal  upon  the  application  of 
similar  treatment.  Cady  also  showed  that  the  electromotive  force  between 
tin  amalgams  in  potassic  stannate,  where  tin  is  quadrivalent,  is  half  that 
observed  in  stannous  chloride.  Lewis,  in  a  paper  published  in  the  Proceed- 
ings of  the  American  Academy  (volume  35,  1899),  independently  arrived 
at  the  same  equation  by  thermodynamic  reasoning. 

Cady's  work  prompted  Trevor"  to  work  out  a  complicated  treatment  of 
the  temperature  coefficient  of  amalgam  cells.  This  paper  is  valuable  from 
the  standpoint  of  pure  mathematics,  but  the  experimental  facts  necessary  to 
verify  his  assumptions  are  not  within  reach  at  present. 

The  next  theoretical  contribution  was  made  by  Haber,"  who  showed  the 
necessity  of  applying  a  new  correction  to  the  calculated  potential  of  sodium 
amalgam  cells.  If  sodium  dissolves  in  mercury  with  the  formation  of 
NaHge,  the  reversible  cycle  described  by  Meyer  must  be  amplified  by  a 
fourth  step — the  reversible  squeezing  out  of  six  mols  of  mercury  from  the 


"  Jahn.  Grundriss  der  Elektrochemie,  p.  8. 

"  Journ.  Phys.  Chem.,  2,  551  (1898).  Attention  should  be  called  to  a  correction  after- 
wards made  in  Cady's  paper,  without  which  it  is  incomplete  and  erroneous  in  one 
feature.    Journ.  Phys.  Chem.,  3,  107  (1899). 

"  Journ.  Phys.  Chem.,  3,  95  (1899). 

"Zeit.  Phys.  Chem.,  41,  399  (1902). 


HISTORICAL   INTRODUCTION.  7 

dilute  amalgam,  and  its  reversible  assimilation  by  the  concentrated.  This 
consideration  raises  the  calculated  electromotive  force  somewhat,  but  Haber 
pointed  out  the  fact  that  the  correction  is  less  than  the  probable  experimental 
error  of  Meyer's  results.  The  possible  effect  of  this  compound  in  causing 
abnormal  osmotic  pressures  was  not  considered,  and  no  new  experimental 
evidence  was  offered.  In  closing  he  entered  a  plea  for  more  accurate  experi- 
mental work  on  concentration  cells  to  verify  his  theoretical  deductions. 

The  nature  and  electrical  behavior  of  cadmium  amalgams  was  the  subject 
of  a  long  and  interesting  paper  by  H.  C.  Bijl,^  published  in  the  same  year. 
Herein  he  recounts  his  measurements  of  the  cells 

Hg,        HggSOi,        CdSO^  solution,        HgCda? 
and 

Hg,        HgjSO^,        CdSO^  solution,        Cd. 

He  constructed  curves  showing  the  effect  of  concentration  and  tempera- 
ture upon  normal  cadmium  elements ;  his  potentials  appeared  to  be  definite 
within  a  tenth  of  a  millivolt — very  accurate  work,  considering  the  experi- 
mental difficulties  presented  by  solid  amalgams.  He  showed  that  in  a  hetero- 
geneous equilibrium  of  liquid  and  solid  cadmium  amalgams  both  phases  had 
the  same  electromotive  force.  Finally,  he  calculated  various  heats  of  amal- 
gamation and  heats  of  crystallization  by  the  method  of  Richards  and  Lewis. 
Owing  to  the  complexity  of  the  phenomena  observed,  his  treatment  of 
results  is  necessarily  empirical,  and  contributes  little  to  the  theoretical  knowl- 
edge of  concentration  effects  per  se. 

In  1903  Roozeboom  and  Van  Heteren,'"  using  the  method  of  Richards  and 
Lewis,  fixed  the  heat  of  amalgamation  of  tin  at  3,000  calories. 

The  subject  received  a  comprehensive  theoretical  treatment  from  the  stand- 
point of  the  Phase  Rule  in  the  same  year  by  W.  Reinders." 

The  most  recent  work  upon  the  subject  is  that  of  J.  F.  Spencer,**  pub- 
lished after  most  of  the  present  work  was  completed.  This  work  is  mainly 
interesting  on  account  of  the  clever  device  used  in  preparing  the  amalgams ; 
but  Spencer  did  not  strive  to  attain  great  accuracy. 


Zeit.  Phys.  Chem.,  41,  641  (1902). 
'Chem.  Cent.  Blatt,  74,  II,  866  (1903). 
'Zeit.  Phys.  Chem.,  42,  225  (1903). 

Zeitschr.  Elektrochem.,  11,  681  (1905)- 


8  ENERGY   CHANGES   INVOLVED   IN   DILUTION    OF  AMALGAMS. 


THE  AIM  AND  SCOPE  OF  THE  PRESENT  RESEARCH. 

The  preceding  review  outlines  the  present  theory  of  amalgam  cells.  No  part 
of  this  theory  has  yet  been  verified  with  the  precision  that  our  present  knowl- 
edge of  absolute  units  would  justify.  The  exactness  of  the  equation  of 
Cady  is  still  somewhat  in  doubt,  and  Haber's  considerations  as  yet  lack 
adequate  experimental  support.  Far  more  pressing  is  a  proof  of  the  pre- 
cision of  the  gas  law  at  infinite  dilution.  This  law  is  a  cornerstone  of 
modem  thermodynamics,  but  its  exact  truth  is  inferred  more  from  extra- 
polation and  analogy  than  from  experimental  data.  These  and  minor  con- 
siderations prompted  the  inception  of  the  present  research. 

To  solve  these  problems  at  all  completely,  the  electrical  measurement 
should  be  accurate  to  one  hundred  thousandth  of  a  volt,  and  the  calorimetric 
determinations  of  the  heats  of  dilution  precise  to  an  equivalent  degree.  With 
such  data  at  hand  a  distinct  advance  can  be  made. 

There  seems  to  be  no  reason  why  the  potential  of  a  given  concentration 
of  liquid  amalgam  at  constant  temperature  should  not  be  perfectly  definite 
when  all  secondary  effects  are  excluded.  On  the  other  hand,  most  solids,  by 
reason  of  their  variable  surface  energy,  do  not  give  very  sharply  defined 
potentials,  and  so  do  not  come  within  the  province  of  this  research. 

Sodium  amalgams,  though  striking  in  their  peculiarities,  are  hard  to  pre- 
pare in  a  state  of  unquestionable  purity,  and  they  react  vigorously  with 
aqueous  solutions.  Unpublished  work  by  Richards  and  Lewis  in  1899  failed 
to  reveal  any  inert  electrolyte  for  use  in  the  cell.  The  method  of  Renter  * 
who  used  alcoholic  solutions  at  — 80°,  is  impracticable  for  accurate  work. 
Hence,  zinc  and  cadmium  amalgams,  which  appear  open  to  neither  of  these 
objections,  are  selected  as  best  adapted  to  the  requirements  of  the  research. 
It  is  true  that  preliminary  experiments  by  the  method  of  Richards  and  Lewis 
seemed  to  indicate  a  slight  reaction  with  aqueous  sulphate  solutions,  even 
when  these  had  previously  stood  in  contact  with  another  sample  of  amalgam. 
But  this  effect  was  finally  referred  to  oxidation  and  carefully  eliminated  in 
a  manner  soon  to  be  described. 


"Chem.  Cent.  Blatt,  73,  II,  1290  (1902). 


THE  VALUES   OF   THE   CONSTANTS.  9 

THE  VALUES  OF  THE  CONSTANTS. 
To  introduce  the  subject  of  potential  measurement,  the  quantities  deter- 
mining IT  in  the  simple  formula  irvF  =  RTln  ^mayi  be  discussed,  with  a  view 

to  discovering  how  closely  the  numerical  values  selected  for  them  may  be 
identified  with  absolute  physical  conceptions.  In  future  the  symbol  tt  will  be 
used  instead  of  E  to  designate  electromotive  force,  in  accord  with  the  more 
general  modern  usage. 

By  the  derivation  of  the  equation  for  monatomic  metals,  v  is  the  valence 
of  the  metallic  ion  in  the  electrolyte  connecting  the  two  amalgams.  Cady's  ^ 
results  are  consistent  with  this  premise,  within  the  limit  of  error  of  his  ex- 
periments, for  the  two  valences  of  tin.  It  is  hard  to  imagine  how  the 
valence  of  the  zinc  or  cadmium  ion  in  a  sulphate  solution  could  be  anything 
else  but  2;  therefore,  in  all  calculations  involving  v,  this  number  will  be 
used. 

Richards  and  Heimrod  "  have  corrected  four  of  the  best  determinations  of 

the  electrochemical  equivalent  of  silver  for  small  chemical  errors.     The  new 

values  were  practically  identical,  in  spite  of  a  great  variety  of  methods  for 

referring  the  strength  of  the  current  observed  to  absolute  units.     Guthe  ^  has 

recently  come  to  the  same  conclusion.     Hence,  great  confidence  is  placed  in 

the  conclusion  that  96,580  coulombs  are  associated  with  a  gram  equivalent 

of  silver.     Richards,  Collins  and  Heimrod,"  and  Richards  and  Stull"  have 

established  the  universality  of  Faraday's  law  upon  a  firmer  basis  than  ever. 

Hence,  the  same  value,  F  =z  96,580,  is  used  for  a  gram  equivalent  of  zinc 

with  reasonable  certainty.     This  value  is  based  upon  the  usually  accepted 

value  107.93  for  the  atomic  weight  of  silver,  and  must  be  diminished  by  0.04 

per  cent  if  silver  is  taken  as  107.89. 

PV 
The  constant  R  is  defined  as  the  quantity  -= ,  expressed  in  mayers,  for  a 

gram  molecule  of  a  perfect  gas  at  any  temperature.  The  recent  work  of 
Daniel  Berthelot  "^  makes  it  probable  that  the  value  of  V  under  760.00  mm.  at 
45°  of  latitude  on  the  sea  level  is  22.412  liters,  and  that  0°  A  =  —  273.08°  C. 
Therefore  these  values  will  be  used  in  the  computations  concerning  a  perfect 
gas,  realizing  that  an  error  of  o.  i  per  cent,  while  improbable,  is  still  possible. 

"•Journ.  Phys.  Chem.  2,  558  (1898). 
■■'Proceedings  of  American  Academy,  37,  415   (1902). 
"*  Physical  Review,  19,  138  (1904). 
"Proceedings  of  American  Academy,  35,  123  (1899). 
""•/fciJ.,  38,  409  (1902). 

"  Daniel  Berthelot,  Trav.  et  Mem.   du  Bureau  internat.   des  poids  et  Mesures,  13, 
113  (1903).     Also  Zeitschr.  Electrochem.,  10,  621  (1904). 


10  ENERGY   CHANGES   INVOLVED  IN   DILUTION   OF  AMALGAMS. 

Upon  this  basis  the  value  of  R  is 

_       76.00  X  13-596  X  980.6  X  22,412 

R  = 5^- — =  8.316  mayers. 

273.08  X  10,000,000  *^  -' 

It  should  be  noted  that  barometric  height  and  the  acceleration  of  gravity 
are  quantities  difficult  to  determine  accurately,  but  they  can  hardly  be  in  such 
serious  doubt  as  V, 

In  applying  the  formula  wvF  =  RTln  -^,  the  above  value  of  R  is  multi- 

plied  by  T,  the  temperature  of  the  cell,  referred  to  the  hydrogen  scale. 
Over  that  part  of  the  scale  used  in  the  following  work  these  readings  are 
essentially  comparable  with  the  corresponding  thermodynamical  tempera- 
tures. Hence  no  uncertainty  is  occasioned  by  the  introduction  of  this 
factor  into  the  formula.     The  experimental  determination  of  temperature 

within  one  one-hundredth  of  a  degree  would  fix  the  value  assigned  to  -^ 

within  I  part  in  30,000.  This  is  far  greater  accuracy  than  can  be  attained 
in  the  determination  of  the  rest  of  the  data  from  which  tt  is  calculated. 

The  most  serious  experimental  uncertainty  lies  in  the  ratio  ^;  this  may 
be  written  as  equal  to  -p'  if  V^  and  Fg  are  respective  volumes  occupied  by 

a  gram  molecule  of  the  dissolved  metal  in  the  two  amalgams.  No  refer- 
ence is  made  to  the  number  of  gram  molecules  of  mercury  involved  in  either 
case. 

Since  tt,  in  volts,  =  0.029  log  ^approximately,  at  20**, 

log^ 

7r=   -^     volts. 

34 

If  the  concentration  ratio  recorded  for  a  given  cell  had  been  o.i  per  cent 

too  small,  the  true  value  of  tt  should  have  been  found  from  the  equation 

_logi.ooi^-i^    log^-1-         log  ,.00, 

""■"  34  34        "^       34 

Since  log  i.ooi  =  0.00044 

TT  =    _^?-ii-     +    0.0000 1    volt. 

34 
Hence  the  calculated  value  of  tt  will  be  in  error  o.ooooi  volt  if  the  concen- 
tration ratio  is  o.i  per  cent  in  error.     Some  serious  obstacles  to  the  determi- 
nation of  the  ratio  with  this  degree  of  precision  will  now  be  considered. 


THE  DENSITY   OF   ZINC   AMALGAMS. 


II 


THE  DENSITY  OF  AMALGAMS. 
Previous  investigators  appear  to  have  mixed  a  weight,  Wj  of  amalgam  of 
concentration  c^  with  a  weight  nW  oi  mercury  to  form  a  new  amalgam  of 
concentration,  Ca ,  and  written 

-^  =w+i. 

This  assumption  is  not  permissible  in  accurate  work,  as  is  shown  by  the 
following  investigation  of  the  densities  of  zinc  and  cadmium  amalgams. 

The  zinc  used  for  this  purpose  was  electrolyzed  from  the  "  chemically 
pure  "  zinc  sulphate  of  commerce,  in  ammoniacal  solution,  and  washed  with 
dilute  ammonia,  distilled  water,  alcohol,  and  ether ;  it  was  dried  in  a  vacuum 
desiccator  over  strong  sulphuric  acid,  to  absorb  all  the  ether  vapor.  The 
mercury  was  shaken  with  strong  sulphuric  acid,  and  passed  through  a 
tower  "  containing  dilute  nitric  acid.  The  materials  were  weighed  out  into 
a  stoppered  tube,  covered  with  dilute  sulphuric  acid,  and  shaken  until  all  the 
zinc  was  dissolved.  The  sulphuric  acid  was  pipetted  off,  neutralized  with 
ammonia,  and  its  zinc  content  determined  by  titration"*  with  a  solution  of 
K4Fe(CN)e,  I  cc.  =  0.003  gram  zinc.  The  proper  correction  was  then 
applied  to  the  weight  of  zinc  taken. 

The  pycnometer  was  of  the  Sprengel  type,  as  modified  by  Ostwald ; "  its 
capacity  was  5  cc,  and  its  tubes  i  mm.  in  diameter.  It  was  treated  with 
cleaning  solution,  and  after  washing  thoroughly,  dried  with  alcohol  and 
ether,  followed  by  suction.  When  all  was  ready,  the  amalgam  was  hastily 
dried  with  filter  paper  and  drawn  into  the  pycnometer ;  the  resulting  oxida- 
tion was  too  small  to  affect  the  density  of  the  product.  The  pycnometer 
was  hung  in  a  large  beaker  of  water  at  a  fixed  temperature  for  a  quarter 
of  an  hour,  after  which  the  surplus  amalgam  was  withdrawn  through  an 
exceedingly  fine  capillary  and  the  glass  was  wiped  with  a  clean  cotton  cloth 


Ostwald-Luther,  Hand-  und  Hulfsbuch,  p.  131  (Leipzig,  1902). 
'de  Koninck  and  Prost,  Zeitschr.  f.  Angew.  Chem.,  1896,  460,  564. 
Ostwald-Luther,  Hand-  und  Hulfsbuch,  p.  142. 


12 


ENERGY   CHANGES   INVOLVED  IN   DILUTION   OF  AMALGAMS. 


and  weighed  at  once.  Since  it  was  hard  to  adjust  the  amalgam  to  the 
mark  as  described  above,  the  length  of  the  surplus  mercury  column  was  care- 
fully measured,  at  times,  and  a  correction  applied  to  the  observed  weight. 
(One  centimeter  of  mercury  in  the  tube  weighs  0.200  gram,  the  mean  of  two 
determinations.)  Corrected  data  are  given  without  comment  in  the  table 
at  the  bottom  of  page  1 1 . 

The  record  of  a  typical  determination  follows: 

( 1 )  Weighing  bottle  +  zii^c  9.8685 

(2)  Weighing  bottle  +  zinc  9.1822 

Weight  of  zinc  0.686 

K4Fe(CN)e  solution  used  =  1.85  cc.    Therefore,  0.006  gram  of  zinc  was 
dissolved  by  sulphuric  acid,  and  must  be  subtracted. 

Weight  zinc  in  amalgam  0.680  gram 

Weight  mercury  in  amalgam  82.12    gram 


Per  cent  zinc  in  amalgam  = 


0.680 
82.80 


82.80 
X  100  =  0.821  (t  =  20°). 


Weight  of  pycnometer  and  amalgam  74.685  to  mark  i. 

Weight  of  pycnometer  7-135 

67.550  to  mark  i. 
The  absolute  density  of  mercury  at  20°  is  13.545." 
.*.  the  density  of  the  amalgam  is 

|^°  X  13545  =  13472+ 

The  table  of  results  follows.  In  the  last  three  calculations  the  assump- 
tion is  made  that  the  coefficients  of  expansion  of  mercury  and  amalgam 
over  4°  are  sensibly  the  same. 

Densities  of  Zinc  Amalgams. 


No. 

l»er  cent  of 

zinc  in 

amalgam. 

to 

Welgrht 
amalgam  in 
pycnometer. 

Weig-ht  mercury 

in  pycnometer 

to  same  mark  at  <©• 

Density 

of  amalgam 

at  20*: 

1 
2 
3 
4 

0.821 
0.644 
0.733 
0.180 

0 

20 
16.4 
16.4 
16.6 

67.550 
67.722 
67.667 
67.914 

67.915 
67.987 
67.987 
67.985 

18.472 
18.493 
13.482 
13.580 

From  these  figures  a  curve  can  be  constructed  giving  the  density  of  any 
zinc  amalgam  between  0.821  per  cent  and  pure  mercury;  some  extrapolation 
would  probably  be  safe  also. 

""  Ostwald-Luther,  Hand-  und  Hulfsbuch,  p.  129. 


THE  DENSITY   OF   ZINC   AMALGAMS. 


13 


The  cadmium  was  electrolyzed  from  a  strong  acid  solution  of  "  chemically 
pure  "  cadmic  sulphate ;  otherwise  the  procedure  was  similar  to  that  described 
for  zinc.  The  weight  of  cadmium  dissolved  in  one  experiment  was  found 
to  be  negligible  for  present  purposes ;  hence  in  succeeding  experiments  the 
titration  was  omitted. 

The  table  of  results  follows: 


Densities 

of  Cadmium  Amalgams. 

No. 

Per  cent  of 

cadmium 

in  amalgam. 

to  of 
thermo- 
stat. 

Weight 
amalg-am  in 
pycnometer. 

Weight  mercury  to 

inner  end  of  mark 

in  pycnometer. 

Density 

of  amalgam 

at3(P. 

1 

1.48 

0 
20.0 

67.518 

67.961 

13.456 

2 

0.74 

20.0 

67.743 

67.961 

13.503 

3 

0.37 

20.0 

67.870 

67.961 

13.527 

4 

2.39 

20.0 

67.257 

67.961 

13.405 

5 

2.97 

20.0 

67.084 

67.961 

13.370 

6 

2.35 

20.0 

67.262 

67.961 

13.406 

Nos.  I,  2,  and  3  were  made  by  dilution  of  amalgams  of  twice  their  re- 
spective concentrations  with  an  equal  volume  of  mercury. 

The  density  curves  are  shown  in  figure  i.  The  dotted  lines  show  the 
average  mixed  density  of  the  unamalgamated  components  calculated  from 
the  following  figures : 

Density  of  zinc  =     7.04 

Density  of  cadmium  =     8.55 
Density  of  mercury  =  13.545 
Consider,  for  example,  the  calculation  of  this  quantity  for  a  3  per  cent 
amalgam  of  cadmium : 

One  hundred  grams  of  the  mixture  contain  3  grams  of  cadmium  and  97 
grams  of  mercury. 


.*.  volume  =  —3 1 

8.55  ^ 


97 


13.545 

Average  density  =  ^Qo-OQ 
7.512 


cc.  =  7.512  cc. 


=  13.312. 


These  dotted  curves  are  very  nearly  straight  lines ;  from  the  portion  of  any 
ordinate  cut  off  between  the  upper  and  the  lower  curve  for  either  metal,  it 
is  easy  to  calculate  the  contraction  which  takes  place  during  the  formation 
of  the  corresponding  amalgam.  Later  these  contractions  will  be  discussed 
in  their  relation  to  various  energy  changes  occurring  in  amalgamation. 

Attention  is  now  called  to  the  method  of  using  the  undotted  actual  curves 
in  calculating  concentration  ratios. 


14 


ENERGY   CHANGES   INVOLVED   IN   DILUTION   OF  AMALGAMS. 


Let  ze/i  be  the  weight  of  amalgam  A^ ,  which  is  diluted  with  w/j  grams  of 
mercury  to  form  a  new  amalgam,  A 2 ;  the  percentage  composition  of  ^2  is 
now  calculated ;  then  the  densities  of  ^^  and  A^  are  found  from  the  curve  to 
be  Di  and  D2 ,  respectively. 

^i  +  «^2 
^'   =  li  =       A       __  e^,  -\-w,  X  j5j . 


a 


A 


ze/, 


n„ 


1336 


1^36 


I3>1^0 


13/^3 


13.44. 


13^^ 


I3A6 


13.50 


i3.se 


11^54 


/ 
/ 
/ 

/ 

/ 

> 
/ 

/ 

/ 

/ 
/ 

/ 

/ 

1 

/ 
/ 

/ 
/ 

/ 
/ 
/ 

/ 

/ 

/ 

/ 
/ 
/ 

/  / 

/ 

/ 

1 

/ 
/ 

/      y 

// 

/   / 

/ 

/ 

/ 

/ 

/ 
/ 

/    / 
/    / 

'/ 

,i^ 

^ 

2.8       3. 


Oyj-  0.8  1.2  1.6  2.0  2.4 

Fig.  I. — The  Densities  of  Zinc  and  Cadmium  Amalgams. 

Density  is  plotted  ordinately;  percentage  composition  in  the  direction  of  abscissae. 

The  shorter  lines  represent  zinc;  the  longer,  cadmium  amalgams.    The  dotted  lines 

give  the  theoretical  values  which  would  be  observed  if  no  contraction  took  place  on 

mixing;  the  continuous  lines  give  the  actual  values. 


THE   PURITY    OF   THE    MATERIALS.  15 

The  factor  ^i  ==  0.995  approximately  when  a  zinc  amalgam  containing 

0.9  per  cent  of  zinc  is  diluted  with  nine  times  its  weight  of  mercury;  the 
same  dilution  of  3  per  cent  cadmium  amalgam  will  introduce  a  factor  of 
0.987.  Neglect  of  this  consideration  makes  the  calculated  values  for  tt  too 
high  in  all  cases,  and  the  error  may  be  a  serious  one. 


THE  PURITY  OF  THE  MATERIALS. 

All  the  materials  used  in  potential  work  were  purified  with  great  care. 
"  Chemically  pure  "  zinc  sulphate  was  dissolved  in  twice-distilled  water  to 
form  a  fairly  strong  solution.  This  was  allowed  to  stand  in  Jena  glass  for 
a  month  over  electrolytic  zinc  made  from  another  sample  of  the  same  salt. 
Fresh  portions  of  zinc  were  added  every  week,  and  the  flasks  were  frequently 
shaken  to  bring  all  parts  of  the  solution  into  contact  with  the  metal.  The 
last  portion  of  zinc  added  was  made  from  a  salt  prepared  for  atomic-weight 
work  in  this  laboratory.'^  The  product  was  filtered  on  pure  filter  papers  and 
recrystallized  three  times  in  platinum.  The  feathery  crystals  obtained  were 
each  time  separated  from  the  mother  liquor  with  great  completeness  by  a 
small  centrifugal "  similar  to  those  used  in  urine  analysis.  The  efficiency 
of  this  device  was  so  great  that  a  cubic  centimeter  of  liquid  could  easily  be 
separated  from  three  times  that  bulk  of  pressed  crystals. 

The  final  product  was  dried  on  a  watch  glass  and  used  in  the  concentra- 
tion cells  without  further  treatment. 

A  generous  supply  of  very  pure  cadmium  sulphate  prepared  for  atomic- 
weight  work  used  was  kindly  placed  at  our  disposal  by  Professor  Baxter 
and  Mr.  Hines.*"  The  sample  in  question  had  been  twice  precipitated  as 
sulphide,  dissolved  in  nitric  acid,  evaporated  with  excess  of  sulphuric  acid, 
three  times  recrystallized,  and  dried  at  100°.  It  was  used  for  the  concen- 
tration cells  without  further  purification. 

The  double  precipitation  as  sulphide  must  have  excluded  those  metals, 
zinc  especially,  which  could  become  sources  of  error  in  the  later  part  of  the 
work. 

Crude  mercury  was  shaken  with  sulphuric  acid  to  remove  the  major  part 
of  its  metallic  impurities.  Then  it  was  vigorously  shaken  for  a  long  time 
with  a  solution  of  mercurous  nitrate  and  nitric  acid  prepared  from  a  sample 

"Richards  &  Rogers,  Proc.  Am.  Acad.,  31,  158  (1895).  This  treatment  is  important 
in  order  to  separate  any  metal  of  less  solution  tension,  which  would  later  replace  zinc 
in  the  amalgam  and  lower  its  electromotive  force. 

"Journ.  Am.  Chem.  Soc,  27,  109  (1905). 

^  Ihid.,  222  (1905). 


l6  ENERGY   CHANGES   INVOLVED   IN   DILUTION    OF  AMALGAMS. 

of  mercury  which  had  undergone  a  similar  purification.  According  to 
Hulett,"  the  resulting  product  should  be  very  pure.  It  was  then  distilled 
under  20  mm.  of  hydrogen  in  an  apparatus  suggested  by  Hulett,  but  improved 
by  the  elimination  of  rubber  joints.  The  hydrogen  generator  used  was  simi- 
lar to  the  one  to  be  described  on  page  19.  A  long  tube  containing  granulated 
calcium  chloride  dried  the  gas  before  it  entered  the  mercury.  All  air  was 
replaced  by  hydrogen  as  completely  as  possible  before  heating  the  mercury. 

The  entire  apparatus  was  one  continuous  piece  of  blown  glass  without  a 
single  piece  of  cork  or  rubber,  as  far  as  the  exhaust  to  the  water  pump.  A 
stopcock  regulating  the  supply  of  gas  bubbling  through  the  mercury  was 
lubricated  with  sirupy  phosphoric  acid.  The  possibility  of  leakage  of  air 
or  the  introduction  of  sulphur  compounds  was  thus  eliminated.  Great  con- 
fidence was  placed  in  the  purity  of  the  product. 

The  materials  thus  described  contained  no  impurities  dangerous  to  the 
success  of  the  potential  measurements.  In  fact,  as  there  was  to  be  measured 
only  a  concentration  effect,  it  seemed  highly  probable  that  pure  materials  of 
commerce  would  have  done  almost  as  well.  A  few  approximate  experi- 
ments, performed  after  the  work  with  pure  materials  was  finished,  tended  to 
bear  out  the  truth  of  this  supposition.  Nevertheless,  it  was  desired  to  run 
no  risks,  and  complete  purity  was  therefore  sought,  as  far  as  possible. 

Water  twice  distilled  in  a  block-tin  condenser  was  used  to  prepare  all 
solutions.  All  vessels  used  in  this  part  of  the  research  were  treated  with 
cleaning  solution  and  well  washed  with  distilled  water;  they  were  dried, 
when  necessary,  by  successive  washings  with  alcohol  and  ether ;  a  current  of 
air  was  finally  sucked  through  them  by  a  filter  pump.  The  alcohol  and  ether 
were  freed  from  water  by  lime  and  calcium  chloride,  respectively.  They  were 
distilled  from  a  glass-stoppered  flask  because  cork  or  rubber  pollute  the  dis- 
tillate. The  delivery  tube  of  the  flask  was  inserted  far  into  the  condenser, 
and  a  light  packing  of  Swedish  filter  paper  discouraged  convection  currents. 
The  products  left  no  residue  on  glass,  and  could  therefore  be  safely  used  for 
drying  purposes. 

An  important  material  was  the  rubber  lubricant,  which  came  into  contact 
with  the  pure  amalgams  and  solutions  during  many  operations  of  the 
research.  Pure  gtim  rubber  was  dissolved  in  its  own  weight  of  hard  paraffin 
by  rubbing  the  heated  mixture  with  a  pestle.  Sufficient  soft  paraffin  was 
then  added  to  bring  the  lubricant  to  the  proper  consistency.  The  whole  was 
then  strained  through  a  clean  cotton  cloth.  It  is  difficult  to  imagine  the 
presence  of  metals,  decomposable  sulphur  compounds,  or  acids  in  the 
product. 

"Zeit.  Phys.  Chem.,  33,  611    (1900). 


THE   PREPARATION   OF  AMALGAMS.  \*J 

PRECAUTIONS  USED  IN  THE  PREPARATION  OF  AMALGAMS. 

Zinc  and  cadmium  amalgams  in  contact  with  air  or  aqueous  solutions  con- 
taining air  are  rapidly  oxidized.  As  early  as  1863  Crova  complained  of  the 
inconstancy  of  the  potential  of  amalgams  "  when  the  proportion  of  the  oxi- 
dizable  metal  is  extremely  small ; "  he  says  that  "  continual  agitation  lessens 
the  error  but  does  not  nullify  it."  St.  Lindeck,  in  1888,  mentions  the  same 
difficulty.  Meyer,  in  1891,  prepared  potassium  and  sodium  amalgams  in  an 
indifferent  gas,  and  delivered  them  through  fine  jets  into  a  solution  free  from 
air.  Richards  and  Lewis  weighed  and  kept  their  zinc  and  cadmium  amal- 
gams under  solutions  of  the  corresponding  sulphate — a  precaution  which 
we  found,  from  preliminary  experiments,  to  retard  oxidation,  but  not  to 
prevent  it  altogether.  Cady  worked  with  amalgams  of  calcium  and  other 
oxidizable  metals  under  pyridin.  In  a  word,  it  appeared  impossible  to 
determine  potentials  within  one  hundred  thousandth  of  a  volt  unless  the 
exclusion  of  oxygen  gas  from  every  part  of  the  process  was  complete.  As 
will  appear  from  the  description  of  the  experiments,  the  success  of  the  follow- 
ing measurements  was  proportional  to  the  completeness  of  this  exclusion. 
Finally  this  cause  of  error  seems  to  have  been  wholly  overcome. 

Clean,  dry  amalgams  of  known  concentration  were  made  from  the  pure 
materials  as  follows : 

The  best  zinc  sulphate  was  dissolved  in  pure  water  to  form  a  saturated 
solution,  which  was  then  somewhat  diluted.  Ammonia  was  generated  in  a 
glass-stoppered  distilling  flask  by  heating  a  strong  commercial  solution  of 
the  gas,  and  passed  into  the  zinc  sulphate  solution  through  a  bent  deliver}' 
tube ;  no  cork  or  rubber  was  used  in  the  apparatus.  A  heavy  precipitate  of 
zincic  hydroxide  redissolved  at  length  to  form  a  clear  solution,  but  the  cur- 
rent of  ammonia  was  continued  a  little  longer  to  avoid  the  formation  of 
zincic  hydroxide  at  the  anode  during  electrolysis.  The  electrodes  were  of 
platinum  foil  about  i  sq.  cm.  in  area.  Platinum  wires  were  welded  to 
them.  Before  using  they  were  boiled  with  strong  nitric  acid  and  washed 
with  distilled  water.  The  current  density  was  large,  but  any  tendency 
to  form  black  or  spongy  deposits  was  carefully  avoided.*"  Since  zinc 
alloys  somewhat  with  a  platinum  cathode,  the  layer  next  the  platinum  was 
not  disturbed.  The  outer  layer  was  removed  from  time  to  time  to  a  beaker 
containing  dilute  distilled  ariimonia.  When  a  sufficient  quantity  had  been 
collected  it  was  washed  on  a  bare  Gooch  crucible  with  dilute  distilled  am- 
monia, distilled  water,  pure  alcohol,  and  ether.  The  crystals  were  then  ex- 
posed over  night  on  a  watch  glass  over  strong  sulphuric  acid  in  a  vacuum 


Proc.  Am.  Acad.,  34,  89  (1898). 


l8  ENERGY   CHANGES   INVOLVED   IN   DILUTION    OF   AMALGAMS. 

desiccator.  In  the  morning  suitable  portions  of  the  zinc  and  of  pure  mercury 
were  weighed  out  into  a  small  tube  provided  with  a  ground-glass  stopper. 

Since  it  proved  difficult  to  combine  dry  zinc  or  cadmium  with  mercury 
without  heating,  it  became  desirable  to  shake  them  together  under  some 
reagent  capable  of  dissolving  the  superficial  film  of  oxide.  The  same  pro- 
cedure was  adopted  in  diluting  some  of  the  amalgams  with  mercury.  Di- 
lute ammonia  is  suitable  for  the  purpose,  because  it  attacks  pure  zinc  and 
cadmium  but  slightly  and  because  the  last  traces  of  it  are  removed  in 
a  vacuum.  The  gas  was  distilled  into  pure  water  until  the  solution  had 
acquired  a  strong  odor.  The  reagent  thus  obtained  was  poured  upon  the 
components  of  the  amalgam  in  the  stoppered  tube,  and  vigorous  shaking  con- 
tinued until  the  process  of  solution  was  complete.  The  analysis  of  the 
aqueous  solution  for  dissolved  zinc  and  cadmium  was  carried  out  volumet- 
rically  with  a  solution  of  potassic  ferrocyanide,  9.6  grains  of  the  crystallized 
salt  per  liter,  a  dilute  copper  sulphate  solution  being  used  as  an  outside 
indicator.  To  standardize  the  ferrocyanide  a  weighed  quantity  of  electro- 
lytic zinc  was  dissolved  in  dilute  sulphuric  acid,  made  up  in  a  graduated 
flask,  and  known  volumes  were  titrated  under  the  conditions  later  prevailing 
in  the  analysis  of  unknown  solutions. 

This  same  ferrocyanide  solution  produces  a  very  insoluble  precipitate  in 

solutions  of  cadmium  salts,  but  the  composition  is  not  Cd2Fe(CN)6,  as  one 

might  expect.*^    The  various  formulas  proposed  by  different  authorities  are 

all    capable    of   generalization    in    the    expression    Cda:Ky[Fe(CN)e]  zz+y. 

4 

Evidently  we  are  dealing  with  a  mixture  or  loose  molecular  compound  of 
Cd2Fe(CN)6  and  CdK2Fe(CN)e  in  proportions  that  vary  considerably 
according  to  concentration  effects  and  temperature.  Under  the  conditions  of 
the  work  here  described,  the  standard  ferrocyanide  solution  was  consistently 
found  by  a  number  of  analyses  to  be  equivalent  to  0.00299  gram  of  zinc  and 
0.0029  gram  of  cadmium  per  milliliter. 

A  dilute  solution  of  ammonia  that  has  been  shaken  with  pure  mercury 
gives  no  precipitate  with  potassic  ferrocyanide ;  therefore  it  is  safe  to  assume 
that  the  zinc  or  cadmium  content  was  determined  by  the  volume  of  ferro- 
cyanide added,  minus  one  final  drop,  whose  size  was  estimated  from  0.0 1  to 
0.04  cc.  according  to  the  volume  of  the  ammonia  solution  and  the  intensity 
of  the  end-point  noted.  The  estimation  was  based  upon  a  series  of  blank 
experiments.  For  some  very  dilute  solutions  an  excess  of  the  ferrocyanide 
solution  was  added  and  the  resulting  opacity  compared  with  a  known  sus- 
pension of  a  second  precipitate.  The  latter  was  diluted  until  equal  opacity 
was  reached,  and  the  familiar  calculation  made. 


"Journ.  Am.  Chem.  Soc,  22,  537  (1900). 


EXCLUSION   OF  AIR   FROM    AMALGAMS. 


19 


The  amalgams  made  up  by  the  method  described  above  were  separated 
from  the  supernatant  liquid  and  bottled  up  clean  and  dry  in  suitable  reser- 
voirs with  the  help  of  the  device  shown  in  figure  2.  G  is  a  hydrogen 
generator  of  the  Richards  type,  in  which  hydrochloric  acid  containing  about 
8  per  cent  of  the  anhydrous  gas  and  the  best  obtainable  grade  of  granulated 
zinc  were  used.  A  trace  of  cupric  chloride  was  added  to  hasten  the  action. 
The  gas  thus  obtained  was  purified  by  passing  it  through  three  Emmerling 
towers,  E^y  E2,  and  E^ ,  each  50  cm.  high  and  5  cm.  in  diameter,  filled  with 
glass  pearls  moistened  with  a  very  strong  solution  of  pure  caustic  soda.  The 
gas  thus  obtained  contains  no  acids  that  might  attack  the  amalgams,  and  is 


Fig.  2. — Device  for  Preserving  Amalgams. 

fairly  dry.  The  pipette  B  is  fused  at  A  to  the  delivery  tube,  and  also  communi- 
cates with  the  vacuum  through  H  and  V.  The  outlet  tube  of  B,  terminating 
in  a  thick-walled  capillary,  passes  through  the  rubber  stopper  K  into  the 
flask  F,  which  is  provided  with  two  sidenecks,  C  and  D;  C  is  fused  to  an 
open  capillary,  and  D  is  connected  with  the  aspirator.  S^ ,  S2 ,  S^ ,  S^,  S^ , 
and  Sq  are  glass  stopcocks  well  lubricated  with  paraffin-rubber  lubricant. 
The  only  rubber  in  the  apparatus  proper,  the  stopper  K,  was  boiled  with 
sodic  hydroxide  solution  and  several  portions  of  distilled  water ;  before  using 
it  was  covered  with  soft  paraffin.  The  consistent  use  of  fused  joints  prevents 
leakage  and  the  introduction  of  sulphur  compounds  from  rubber. 


20 


ENERGY   CHANGES   INVOLVED   IN   DILUTION   OF  AMALGAMS. 


The  apparatus  thus  arranged  and  scrupulously  clean  and  dry  is  manipu- 
lated as  follows :  First,  S-^ ,  S2 ,  and  S^  are  closed,  and  S^ ,  S^  ,  and  S^  left 
open ;  the  pressure  in  B  and  F  is  reduced  to  i  or  2  cm.  of  mercury,  after 
which  the  rubber  tube  V  is  clamped  off  beyond  M  to  test  for  leakage.  If  M 
remains  at  exactly  its  original  height  for  one  minute  it  is  assumed  that  no 
leakage  occurs.  Then  S^  is  closed,  and  S^  cautiously  opened,  filling  the 
system  with  hydrogen.  This  operation  is  performed  three  times,  after 
which  the  air  in  the  capillary  C  is  expelled  by  a  stream  of  hydrogen.  Then 
5*5  and  S^  are  closed,  and  S^  opened,  exhausting  F  once  more ;  the  tube  C 
is  then  plunged  below  the  surface  of  the  amalgam  under  ammonia  in  the 
weighing  tube,  and  S^  cautiously  opened.  In  this  way  all  the  amalgam  can 
be  sucked  into  the  flask  practically  free 
from  moisture.  As  the  last  of  it 
passes  S^  the  flow  is  stopped.  Main- 
taining a  low  pressure  in  F,  a  rapid 
stream  of  hydrogen  gas  is  bubbled 
through  the  amalgam  to  mix  it  and  to 
eliminate  the  last  traces  of  water  and 
ammonia.  After  five  or  ten  minues  ^'3 
is  closed,  and  F  filled  with  hydrogen  ; 
Si  and  S^  are  closed  and  B  evacuated 
through  5*2.  Then  5*4  is  cautiously 
opened,  and  the  amalgam  sucked  into 
B,  filling  not  more  than  10  per  cent  of 
the  entire  volume.  The  vacuum  is 
now  shut  oflF,  and  B  filled  with  hydro- 
gen communicating  with  the  outside 

air  through  ^2 .  The  tube  A  can  now  be  sealed  off  from  the  generator  with- 
out admission  of  air.  Its  end  is  bent  into  a  hook  to  allow  of  suspension 
from  a  balance.  Tube  D  is  cut  with  a  file,  and  B  detached  from  F.  The 
pipette  is  labeled  and  placed  in  a  rack  with  its  fellows  (figure  3).  The 
ammonia  in  C  is  added  to  the  main  portion  in  the  weighing  tube,  and  titrated 
as  before  described. 

Amalgams  prepared  in  this  way  are  perfectly  clean  and  bright  and  remain 
so  indefinitely.  The  weight  of  the  column  in  the  outlet  tube  permits  the 
withdrawal  of  practically  all  the  amalgam  when  the  stopcock  is  opened. 
No  access  of  air  is  possible  except  at  the  very  small  surface  at  the  end  of 
the  capillary  E,  and  even  this  small  effect  can  be  eliminated  by  running  out 
a  drop  of  amalgam  before  beginning  a  determination. 

The  solution  of  zinc  or  cadmium  sulphate  was  freed  from  air  in  the  appa- 
ratus just  described.     The  liquid  was  introduced  into  the  flask  F  like  an 


Fig.  3. — Rack  with  Pipettes 
Containing  Amalgams. 


THE    CELL   AND   ITS   MANIPULATION.  21 

amalgam,  then  with  S^  open  to  the  vacuum  a  rapid  stream  of  rarefied 
hydrogen  was  passed  through  the  solution  for  some  time.  It  is  believed 
that  this  process  removed  the  remaining  air.  Finally  S^  was  closed,  and  F 
allowed  to  fill  with  hydrogen,  after  which  the  solution  was  drawn  up  into  B 
in  the  usual  way.  When  the  connection  at  A  was  fused  off,  the  outlet  of  B 
was  drawn  out  into  a  fragile  capillary  and  sealed.  Of  course,  when  the 
solution  was  wanted,  its  weight  was  not  sufficient  to  draw  it  out.  To  follow 
it  up  with  hydrogen  a  well-cleaned  rubber  tube  delivering  hydrogen  was 
forced  over  the  fragile  capillary ;  when  this  was  broken  communication  with 
the  gas  generator  was  established. 

Some  previous  investigators  have  allowed  their  electrolytes  to  stand  over 
amalgams  for  some  time  before  using  it  in  the  cells."  Zinc  sulphate,  fifth 
normal,  was  left  in  Jena  glass  over  amalgam  of  the  purest  materials  for 
several  weeks  before  the  first  measurements,  with  occasional  stirring.  Per- 
haps the  partial  absorption  of  dissolved  oxygen  by  the  amalgam  thus  attained 
is  helpful.  However  this  may  be,  a  pure  sulphate  solution  freed  from  air  by 
a  stream  of  hydrogen  can  be  used  with  perfect  safety  without  putting  it 
through  this  lengthy  process. 

THE  CELL  AND  ITS  MANIPULATION. 

The  cells  used  in  the  potential  measurements  must  now  be  described. 
Figure  4  gives  a  good  idea  of  the  appearance  of  one  of  these  just  after  a 
determination.  The  other  cell  used  was  different  in  one  respect — its  cups 
were  all  the  same  size.  Very  careful  annealing  of  this  apparatus  is  neces- 
sary. The  advantages  of  this  arrangement  are  marked.  Four  different 
amalgams  can  be  introduced  at  one  filling,  and  six  direct  potential  measure- 
ments obtained  under  exactly  the  same  conditions.  Great  economy  of  time 
and  material  are  thus  secured,  and  more  important  still,  valuable  checks  on 
the  accuracy  of  the  measurements.  These  will  be  discussed  later.  The  prin- 
ciple might,  if  necessary,  be  extended  to  cells  containing  even  more  cups. 

The  cell,  clean  and  dry,  was  suitably  supported  in  the  thermostat,  and 
the  tube  A  fused  to  the  outlet  of  a  hydrogen  generator  similar  to  that  shown 
in  figure  2,  and  like  it  made  of  a  single  piece  of  glass.  A  double  gridiron 
of  glass  tubing  allowed  considerable  play  without  the  introduction  of  a  rub- 
ber connection,  but  the  tubes  B,  C,  D,  E,  were  closed  by  clean  rubber  tubes 
and  pieces  of  glass  rod.  The  rubber  surface  exposed  to  the  atmosphere  of 
the  cell  was  very  small.  The  system  as  far  back  as  the  stopcock  S^  was 
evacuated  through  S^  by  a  very  efficient  mechanical  hand  pump,  and  then 
filled  with  hydrogen  through  S^ .     After  this  operation  had  been  performed 

"Richards  and  Lewis,  Proc.  Am.  Acad.,  34,  87  (1898). 


22 


ENERGY   CHANGES   INVOLVED   IN   DILUTION   OF  AMALGAMS. 


three  times,  one  of  the  glass  rods  was  removed  and  the  tip  of  the  solution 
pipette  inserted  while  hydrogen  was  issuing  from  the  fine  opening.  The 
issuing  stream  of  hydrogen  prevented  the  diffusion  of  air  into  the  cell. 
When  the  body  of  the  cell  was  about  half  full,  the  solution  pipette  was  with- 
drawn and  the  various  amalgam  pipettes  successively  inserted  in  the  tubes 
B,  C,  D,  E,  Suitable  portions  of  the  amalgams  were  run  in.  Finally  the 
platinum  electrode  wires,  sealed  into  tapering  glass  tubes,  were  introduced, 
and  the  cell  was  ready  for  use. 


4. — Amalgams  in  Cell  Ready  for  Potential  Measurement. 


The  temperature  of  the  thermostat  was  kept  constant  within  a  hundredth 
of  a  degree  by  the  familiar  electrical  regulating  device  shown  in  the  dia- 
gram (figure  5).  The  mercury  column,  instead  of  cutting  off  a  gas  supply 
at  Q,  cuts  off  the  current  through  the  incandescent  lamp  hung  in  the  water 
until  the  water  cooled  sufficiently  to  allow  the  circuit  to  be  broken  again 
at  Q.  An  efficient  centrifugal  stirrer  operated  by  a  small  electric  motor 
kept  the  water  in  rapid  circulation.  The  variation  in  temperature  noted  on 
a  sensitive  Beckmann  thermometer  graduated  to  one-hundredth  never  ex- 
ceeded five  one-thousandths  of  a  degree.  Although  it  was  not  important  to 
know  the  temperature  of  the  cell  within  nearer  than  0.05°  it  was  nevertheless 


THE   POTENTIOMETER.  23 

necessary  that  the  different  amalgams  should  be  maintained  at  exactly  iden- 
tical temperatures ;  hence  the  care  taken  about  this  point. 

The  centigrade  temperature  was  read  from  a  thermometer  graduated  to 
tenths  of  a  degree  and  permitting  the  estimation  of  hundredths,  which  was 
compared  from  time  to  time  with  a  Reichsanstalt  thermometer.  The  zero 
point  of  the  latter  was  determined  in  ice  and  distilled  water.  Small  correc- 
tions to  the  bore  had  been  determined  by  comparison  with  a  very  accurate 
Baudin  thermometer. 

THE  POTENTIOMETER  AND  ITS  CALIBRATION. 

The  potentiometer  shown  in  figure  5  was  designed  to  give  direct  readings 
accurate  to  a  few  millionths  of  a  volt.  A  fall  of  potential  of  i  volt  in  the 
10,000  ohms  between  B  and  P  corresponds  to  0.00000 1  volt  for  each  o.oi 
ohm ;  therefore,  to  attain  the  required  degree  of  precision,  all  resistances  to 
be  included  between  the  poles  of  unknown  cells  must  be  known  within  a  few 
hundredths  of  an  ohm.  Since  not  more  than  one-twentieth  of  the  entire  fall 
of  potential  was  ever  neutralized  in  this  manner,  the  other  parts  of  the 
system  need  be  standardized  only  one-twentieth  as  carefully.  As  a  matter 
of  fact  the  box  A,  containing  nine  lOO-ohm  coils  and  ten  lo-ohm  coils,  was 
calibrated  to  0.0 1  ohm,  and  the  external  resistances  to  o.i  ohm.  For  the 
purpose  a  method  of  substitution,  very  similar  to  one  recommended  by 
Ostwald,"  was  adopted.  In  each  comparison  all  four  arms  of  the  comparing 
bridge  were  of  the  same  order  of  magnitude,  so  that  the  most  sensitive  and 
reliable  adjustment  was  secured.  All  connections  whose  resistance  could 
influence  the  results  were  made  with  great  care.  Extra  heavy  brass  con- 
nectors were  clamped  upon  the  polished  pegs  of  box  A  with  the  help  of 
pliers;  heavy  copper  wires  were  used  as  leads,  and  their  ends  were  either 
soldered  or  amalgamated  and  dipped  in  the  mercury  cups  of  the  rocker  switch. 
The  plugs  used  in  comparing  the  bridge  box  were  polished  and  driven  home 
so  well  that  the  total  resistance  of  the  bars  and  connections  measured  only 
0.006  ohm — a  negligible  amount.  Heavy  wires  were  used  in  the  rocker 
switch,  and  all  their  joints  were  soldered. 

The  table  of  corrections  was  constructed  as  if  the  resistances  had  been 
weights,"  the  unit  of  reference  being  the  value  of  the  whole  potentiometer 
box  as  1,000  nominal  ohms.  The  accuracy  of  the  table  was  established  in  a 
wholly  satisfactory  manner  by  the  direct  comparison  of  several  nominally 
equal  combinations ;  in  every  case  the  observed  results  coincided  with  those 
predicted  from  the  table. 


Ostwald-Luther,  Hand-  und  Hulfsbuch,  p.  355. 
Richards,  Journ.  Am.  Chem.  Soc,  22,  144  (1900). 


24 


ENERGY   CHANGES   INVOLVED   IN   DILUTION   OF  AMALGAMS. 


THE   POTENTIOMETER. 


25 


A  troublesome  problem  was  encountered  in  the  division  of  the  lo-ohm 
coils  of  box  A  into  100  parts  to  read  to  hundred  thousandths  of  a  volt.  At 
£rst  it  was  thought  that  the  double  shunt  device  suggested  by  Richards  and 
Lewis  *^  for  the  same  purpose  would  be  sufficient. 

The  shunts  were  both  standardized  and  a  complicated  method  of  applying 
the  corrections  worked  out.  Needless  to  say,  the  labor  of  adjusting  this 
device  was  severe;  but  unfortunately  the  results  obtained  with  it  were  not 
wholly  consistent.  For  instance,  the  cups  of  the  cell  were  filled  with  vari- 
ous amalgams,  which  we  will  call  A,  B,  C,  and  D.  The  potentials  between 
A  and  B,  B  and  C,  and  C  and  D  were  separately  determined,  corrected, 
and  added  up.  Then  the  potential  between  A  and  D,  derived  in  the  same 
manner,  was  compared  with  this  sum.  The  resulting  values  were  re- 
spectively 0.05085,  and  0.05081  nominal  volt.  Other  similar  experiments, 
liardly  more  satisfactory  than  the  one  just  described,  led  us  to  abandon  the 
method.  Probably  the  fault  lies  in  the  excessive  number  of  movable  con- 
nections necessary  in  the  apparatus,  which  answers  well  when  less  accuracy 
is  demanded. 

The  final  arrangement  is  shown  in  figure  5.  MN  is  a  manganin  wire  of 
nearly  10  ohms  resistance  and  90  cm.  in  length ;  its  extremities  are  soldered 
to  the  upper  surfaces  of  the  brass  plates  at  M  and  N.  A  long  strip  of  glass 
fits  accurately  between  these,  and  forms  a  satisfactory  bed  for  the  wire. 
The  whole  is  mounted  upon  a  well-seasoned  slab  of  whitewood,  bearing  a 
scale  which  divides  MN  into  100  equal  parts.  A  heavy  copper  wire  is  sol- 
dered at  one  end  to  M,  and  at  the  other  to  the  heavy  brass  connector  F, 
which  can  be  clamped  firmly  upon  any  lo-ohm  peg  in  the  box  A.  N  was 
connected  to  a  resistance  box,  C,  which  contained  10,  20,  30,  and  40  ohm  coils. 
The  resistance  from  P  to  U,  plus  the  small  coil  R,  plus  the  slider,  equals 
nine  times  the  resistance  of  box  A,  If,  however,  the  movable  connector  Y 
is  moved  from  its  present  position  in  the  course  of  a  measurement,  n  times 
10  ohms  are  cut  out  of  the  circuit.  To  maintain  the  rate  of  fall  of  potential 
at  its  original  value,  the  proper  resistance  is  introduced  from  C. 

L  was  a  Leclanche  cell,  whose  potential  was  about  1.4  volts ;  its  current  ran 
through  the  parts  of  the  system  so  far  described,  and  also  through  a  variable 
resistance,  E,  of  about  4,200  ohms.  By  properly  adjusting  E,  the  potential 
between  B  and  P  could  be  made  equal  to  that  of  the  i-volt  cell  V  within  i 
part  in  14,000.  The  switch  S^  is  thrown  toward  K^ ,  and  when  the  i-volt  cell 
was  just  balanced  by  the  fall  of  potential  between  B  and  P,  no  deflection  of 
the  galvanometer  G  was  noted  on  closing  the  key  K^ .  The  Helmholtz  cell  V 
was  made  with  great  care  from  pure  materials,  as  recommended  by  Ostwald," 

*'Proc.  Am.  Acad.,  34,  91   (1898). 

*^  Ostwald-Luther,  Hand-  und  Hiilfsbuch,  p.  364. 


26  ENERGY   CHANGES   INVOLVED   IN   DILUTION   OF  AMALGAMS. 

and  its  potential  was  very  constant,  though  not  exactly  equal  to  i  volt.  Its 
standardization  will  be  considered  on  page  29. 

The  galvanometer  G  was  a  sensitive  instrument  of  the  d'Arsonval  type.  Its 
resistance  was  nearly  300  ohms.  The  glass  front,  which  was  imperfect,  was 
removed,  and  the  galvanometer  was  completely  inclosed  in  a  tight  wooden 
box  not  shown  in  the  diagram.  A  small  window  of  optical  glass  was  placed 
in  the  side  of  the  box  opposite  the  mirror,  and  the  opposite  wall  was  cov- 
ered with  black  paper.  The  influence  of  drafts  and  of  annoying  reflections 
was  thus  avoided.  Deflections  were  observed  through  a  telescope,  T,  com- 
bined with  a  graduated  scale ;  the  portion  of  this,  whose  reflection  was  seen 
in  the  telescope,  was  illuminated  by  a  small  gas  flame,  Fj  placed  at  a  safe 
distance  from  any  junction  of  unlike  metals.  A  thousand  ohms  could  be 
introduced  into  the  galvanometer  circuit  by  means  of  the  switch  ^2  when 
circumstances  required  it.  The  whole  apparatus  was  set  up  in  a  room  of 
constant  temperature. 

The  cell  for  containing  the  amalgams  and  the  method  followed  in  setting 
it  up  have  already  been  described.  The  terminal  wires,  with  great  care  to 
avoid  momentary  short  circuits,  were  attached  to  brass  binding  posts,  J^ 
and  J 2 ,  mounted  on  an  ebonite  base  clamped  to  the  rim  of  the  thermostat. 
The  resistance  in  E  was  now  adjusted  as  previously  described,  after  which 
the  switch  S^  was  thrown  over  toward  K2 .  Then  the  potential  of  the  un- 
known cell  was  neutralized  within  a  millivolt  by  placing  the  connectors  Y 
and  Z  on  the  proper  pegs,  y  and  z,  of  box  A.  After  this  approximate  ad- 
justment, the  compensation  of  potential  was  completed  by  moving  the  plati- 
num contact  F  along  the  slide  wire  MN  until  on  pressing  the  key  K2  no 
deflection  was  noted  in  the  galvanometer.  Positive  indications  could  be 
obtained  from  this  instrument  from  changes  in  the  position  of  the  slider 
corresponding  to  five  millionths  of  a  volt.  Therefore,  no  interpolation  was 
necessary  to  get  the  fifth  place  correct  to  within  half  a  unit.  To  make 
assurance  doubly  sure,  a  point  five  millionths  of  a  volt  on  either  side  of  the 
zero,  giving  swings  of  the  galvanometer  in  opposite  directions,  was  always 
noted. 

The  total  value,  x,  of  the  slider  was  determined  under  the  conditions 
actually  prevailing  in  potential  measurement.  A  certain  cell  was  made  to 
read  very  nearly  0.03200  nominal  volt  by  suitably  adjusting  its  temperature. 
The  following  readings  were  then  obtained : 

Box  A.  Corrected. 

(i)     TT  =  0.03300-1- 0.025 ;r  T=: 0.032984  + 0.025  ;jr 

(2)     nz=  0.03200 -{-X  7r=:o.o3i99  -^x 


THE   POTENTIOMETER. 


27 


Therefore  by  subtraction  we  have  0.000994  =  0.975  '^' 

Hence  the  fall  of  potential  from  one  end  of  the  slider  to  the  other  is 
0.00102  volt. 

The  scale  of  the  slider  was  calibrated  with  the  help  of  a  small  potentio- 
meter box,  carefully  standardized,  containing  ten  2-ohm  coils.  The  extremi- 
ties of  the  slider  were  soldered  to  the  terminals  of  this  box  by  heavy  copper 
wires ;  after  equilibrium  of  temperature  was  assured,  the  poles  of  a  battery 
were  attached  at  these  points.  Then  with  the  help  of  a  sliding  contact  con- 
nected through  a  galvanometer  to  the  various  pegs  on  the  box,  nine  points  on 
the  slide  wire  were  found  where  no  deflection  was  noted.  These  could  be 
referred  to  the  known  resistances  of  the  bridge,  and  their  error  determined. 
The  determination  was  then  repeated  with  the  box  reversed.  Because  the 
slight  corrections  thus  found  were  regular,  it  was  assumed,  as  seems  per- 
missible, that  the  variation  of  the  wire  between  these  points  proceeded 
at  a  uniform  rate.  The  two  errors  of  the  slider  can  now  be  combined  and 
corrected  for  together. 


Reading  on 
slider. 

Corrrection 

Correction 

Total 

due  to 

due  to 

correction  in 

whole  wire. 

error  of  scale. 

volts  X  10-6 

10 

+  0.3 

+  0.0 

+  0.2 

20 

+  0.4 

-0.2 

+  0.2 

30 

+  0.6 

-0.2 

+  0.4 

40 

+  0.8 

-0.3 

+  0.5 

50 

+  1.0 

-0.4 

+  0.6 

60 

+  1.2 

-0.3 

+  0.9 

70 

+  1.4 

-0.3 

+  1.1 

80 

+  1.6 

-0.3 

+  1.3 

90 

+  1.8 

-0.3 

+  1.5 

100 

+  2.0 

±0.0 

+  2.0 

These  values  were  used  in  the  work  on  zinc.  Eight  months  elapsed  be- 
tween the  work  on  zinc  and  that  on  cadmium,  and  after  that  time  the  slide 
wire  showed  traces  of  corrosion.  It  was  polished  with  very  fine  sandpaper 
and  then  restandardized  with  the  same  precautions  as  before. 


Reading  on 
slider. 

Cadmium  meas- 
urements. 
Correction  in 
volts  X  10-6. 

Reading  on 
slider. 

Cadmium  meas- 
urements. 
Correction  in 
volts  X  10-6. 

10 

+  0.3 

60 

+  1.4 

20 

+  0.4 

70 

+  1.5 

30 

+  0.7 

80 

+  1.8 

40 

+  0.9 

90 

+  2.8 

50 

+  1.1 

100 

+  2.6 

20  ENERGY   CHANGES   INVOLVED   IN   DILUTION   OF   AMALGAMS. 

The  most  serious  sources  of  accidental  error — partial  short  circuiting  of 
points  differing  widely  in  potential,  and  thermoelectric  currents — were  con- 
stantly borne  in  mind.  All  switches  and  keys  were  mounted  on  glass,  and 
all  wires  not  carried  in  air  lines  were  encased  in  glass  tubes  throughout  their 
entire  length.  The  apparatus  was  set  up  in  a  dry  basement  room  which 
responded  slowly  to  outside  temperature  changes.  The  absence  of  thermo- 
electric effects  had  to  be  inferred  rather  than  proved.  Brass,  copper,  and 
manganin,  which  have  very  small  thermoelectric  forces  against  each  other,** 
formed  most  of  the  circuit,  while  platinum  and  German  silver  were  sparingly 
used,  and  opposite  junctions  with  other  metals  were  always  close  together. 
Finally,  the  disposition  of  the  apparatus  seemed  to  offer  no  opportunity  for 
large  permanent  temperature  differences  at  various  points. 

Boxes  A  and  D  were  of  manganin ;  A  was  at  least  eight  years  old  and  D 
almost  as  well  aged.  Hence  the  relative  values  of  the  resistances  can  be 
assumed  as  constant  over  long  periods. 

THE  STANDARD  OF  POTENTIAL. 

All  was  now  ready  to  measure  the  potential  of  concentration  cells  with  an 
actual  error  not  greater  than  five  millionths  of  the  i-volt  cell.  Evidently  the 
latter's  value  in  absolute  units  must  be  known  as  accurately  as  possible.  The 
standard  at  first  relied  upon  was  a  large  Clark  cell  of  the  usual  form,  bearing 
the  stamp  of  the  Reichsanstalt.  As  it  had  been  in  the  laboratory  for  six 
years,  it  seemed  wise  to  verify  the  statement  of  its  potential  as  found  in  its 
certificate.  Immediately  after  the  close  of  the  measurements  on  zinc,  Pro- 
fessor B.  O.  Peirce,  of  the  Department  of  Physics  in  Harvard  University, 
examined  it  with  great  care,  a  service  for  which  we  are  deeply  indebted. 
His  conclusions  are  quoted  from  his  letter  as  follows : 

A  hasty  comparison  made  on  Saturday  of  your  normal  Clark  element  with  two 
standard  cadmium  cells,  presumed  to  have  the  E.  M.  F.  of  1.0186  volts  at  21**,  gave  as 
the  E.  M.  F.  of  the  former  1.420-f-  at  21.5**.  A  more  careful  comparison  made  to-day 
gave  1.4206  with  each  cell  at  21.5°,  and  since  the  element  has  been  kept  at  practically  a 
constant  temperature  for  some  time,  the  effect  of  time-lag  may  be  assumed  to  have 
disappeared. 

I  tested  also  five  Carhart-Clark  cells,  and  found  that  these  differed  considerably 
among  themselves.  As  the  E.  M.  F.  of  such  a  cell  is  likely  to  fall  off,  as  times  goes  on, 
I  chose  that  which  had  the  highest  E  M.  F.,  and  using  Carhart's  certificate  of  1.4400 
— 0.00056  {t — 15)  as  the  E.  M.  F.,  got  the  same  value  as  before  (1.4206  international 
volts  at  21.5")  for  the  E.  M.  F.  of  your  element. 


"Landolt  und  Bomstein  (Meyerhoffer)  Tabellen,  p.  776  (1905)- 


THE   STANDARD  OF   POTENTIAL.  29 

In  other  words,  the  electromotive  force  of  our  standard  has  fallen  off 
several  tenths  of  i  per  cent  from  the  value  required  by  the  Reichsanstalt 
formula  for  a  Latimer-Clark  cell  at  this  temperature.  Several  days  later,  in 
reply  to  some  inquiries  concerning  the  variability  of  Clark  cells  of  this  type, 
Professor  Peirce  made  a  second  very  instructive  investigation  of  this  and 
other  similar  cells.     He  wrote  as  follows : 

...  I  first  tested  against  a  certain  cell  used  as  a  makeweight  the  four  Muirhead 
standard  cells,  10915I,  13361I,  logisr,  13361T,  received  a  few  months  ago  from  the 
Cromptons  to  serve  as  standard  units,  with  a  very  elaborate  potentiometer  made  and 
tested  by  them.  The  readings  were  1.4223,  1.4236,  1.4219,  1.4243,  the  cells  being  at 
22.5"  C.  Your  cell,  which  had  been  at  20.6°  for  some  time,  gave  a  reading  of  1.4226 
and  a  cadmium  cell  gave  1.0191.  You  will  notice  the  comparatively  large  difference 
between  the  English  cells,  which  are  from  a  famous  maker  and  have  been  tested  by  a 
well-known  firm  of  electrical  engineers.  If  10915,  as  is  probable,  was  made  before 
13361,  the  fall  of  E.  M.  F.  with  age  seems  to  be  indicated. 

Of  the  Clark-Carhart  cells  A  and  B  are  seven  or  eight  years  old,  I  think;  264  and 
265  are,  I  believe,  more  than  six  years  old;  702,  706,  735,  737,  and  740  are  new  (the 
oldest  bears  the  date  February  18,  1902,  and  carries  a  guarantee  with  proper  treatrnent 
for  three  years,  but  I  can  not  be  sure  that  the  laboratory  has  never  fallen  below  allow- 
able temperatures) .    The  potentiometer  readings  were,  at  temperature  in  cells  of  23.5° : 

A        1.4257  265        1.3939  735        1.4335 

B        1.4202  702        1.4337  737        1.433s 

264        1.4260  706        1.4314  740        1.4325 

The  effect  of  age  or  wear  and  tear  due  to  temperature  changes  and  not  to  polariza- 
tion in  use  seems  clear. 

Our  cadmium  cells  are  all  almost  exactly  alike,  and  if  for  the  sake  of  argument  we 
assume  that  the  E.  M.  F.  of  any  one  of  them  at  room  temperatures  was  1.0185  true 
volts,  and  apply  to  them  the  slight  temperature  correction  called  for  by  the  formula, 
the  best  two  Muirhead  cells  would  have  R  M.  F.s  of  about  1.4241  and  1.4248  at  21.5°, 
where  the  formula  calls  for  1.4248  true  volts.  The  best  three  Carhart-Clark  cells  would 
have  at  21.5**  E.  M.  F.s  of  about  1.434  instead  of  1.436,  and  your  cell  would  have  at 
21.5°,  the  E.  M.  F.  1.4206,  which  was  nearly  what  I  got  the  other  day. 

Professor  Peirce's  exhaustive  work  establishes  our  potential  standard  be- 
yond the  possibility  of  doubt. 

The  formula  used  for  the  temperature  coefficient  Trjo^TTigo — 0.0012 (^ — 15) 
is  substantially  the  same  as  that  given  by  the  Reichsanstalt. 

The  comparison  of  the  i-volt  cell  with  the  standard  Clark  element  was 
made  on  the  standardized  potentiometer  already  described,  in  the  usual  way. 

After  the  reading,  the  i-volt  cell  was  returned  to  its  original  position  to 
prove  that  the  potential  of  the  Leclanche  cell  had  remained  constant. 

Professor  Peirce's  value  for  the  Clark  cell,  corrected  for  its  temperature 
coeflficient,  time-lag  being  eliminated  as  nearly  as  possible,  established  the 
potential  of  the  i-volt  cell  as  follows: 


30 


ENERGY   CHANGES   INVOLVED   IN   DILUTION  OF  AMALGAMS. 


Electromotive  Force  of  Standard  Helmholtz  Cell. 


No. 

Time  of  observation. 

T.  of  Clark  cell. 

Xatto. 

1 
2 
3 
4 

Before  work  on  zinc 

After  three  measurements.. . 
After  seven  measurements.. 
Near  end  of  work 

19.7° 
20.2 
22.6 
20.6 

0.9924  at  21° 
.9925  at  20 
.9927  at  24 
.9926  at  21 

TT  =  0.9925  at  21° 

The  average,  X  =  0.9925  +  0.00007  {t  —  21°)  international  volts,  is  safe 
to  use  on  all  measurements  of  zinc  concentration  cells. 

Eight  months  elapsed  before  the  final  determinations  on  cadmium  concen- 
tration cells  were  made.  Standardizations  against  the  Clark  cell  now  gave 
inconstant  results,  apparently  due  to  the  more  rapid  temperature  changes  of 
the  laboratory  during  the  winter.  The  average  of  four  determinations  indi- 
cated that  X  =  0.9931  volt  at  19°.  It  seemed  unlikely  that  the  Helmholtz 
cell  had  changed  as  much  as  this ;  but  on  the  other  hand,  the  Clark  cell  was 
known  to  have  fallen  off  considerably  in  six  years,  and  may  well  have  con- 
tinued to  do  so  since  its  standardization  in  June.  Finally  Mr.  R.  W.  Kent, 
of  this  laboratory,  kindly  lent  two  cadmium  cells,  carefully  made  up  from 
pure  materials  as  recommended  by  Carhart  and  Hulett "  and  at  least  a  week 
old.  When  opposed  to  the  i-volt  cell,  they  each  gave  very  nearly  0.0261 
of  X,  which  was  measured  on  the  potentiometer  like  the  electromotive  force 
of  a  concentration  cell.  Using  the  formula  tt  =  1.0186  +  0.00004  (20  —  t) 
international  volts,"  a  potential  X  ^=  0.9927  was  established  for  the  i-volt  cell 
at  19°.  This  value  is  practically  the  same  as  that  observed  in  June.  It 
appeared  more  reliable  than  the  slightly  different  verdict  of  the  Clark  cell, 
and  was  adopted  for  all  measurements  on  cadmium  concentration  cells, 
X  =  0.9927  -f  .00007  (^  — 19°)- 


THE  ELECTROMOTIVE  FORCE  BETWEEN  ZINC  AMALGAMS. 

The  work  on  zinc  amalgams  is  conveniently  considered  first.  Before  pre- 
senting the  quantitative  data,  a  few  more  details  must  be  reviewed. 

All  the  zinc  amalgams  were  made  by  successive  dilutions  of  two  liquid 
amalgams,  No.  i  and  No.  3,  both  of  which  were  made  from  zinc  and  mercury. 
There  was  some  question  as  to  the  accuracy  with  which  the  pure  zinc 
described  above  could  be  weighed  out ;  hence  the  true  concentration  ratio  of 
No.  I  and  No.  3  was  not  known  with  as  much  precision  as  could  be  attained 
in  the  dilution  of  each  separated.     Direct  evidence  could  have  been  secured 

**  American  Electrochemical  Society  Trans.,  5,  59  (1904). 
*"  Ostwald-Luther,  Hand-  und  Hulfsbuch,  p.  362. 


MEASUREMENTS   WITH   ZINC   AMALGAMS.  3I 

by  a  potential  measurement,  calculating  ^    from  the  equation  in  which 

IT  and  T  were  known.  As  this  was  not  done,  no  amalgam  derived  from  No.  3 
was  ever  measured  against  any  derived  from  No.  i.  Two  independent  sets  of 
results  were  thus  secured,  which  by  their  agreement  established  certain  con- 
clusions beyond  a  reasonable  doubt. 

The  possibility  of  polarizing  the  most  dilute  amalgams  during  measure- 
ments was  considered.  Momentary  currents  ranging  from  0.00 1  to  o.ooooi 
volt  and  flowing  in  alternate  directions  through  a  resistance  of  a  thousand 
ohms  can  transfer  only  infinitesimal  amounts  of  zinc.  Still,  the  expected 
potential  was  roughly  calculated  before  measurements,  to  avoid  excessive 
differences  at  the  first  contact,  and  before  the  final  readings  were  made  the 
cell  was  shaken  to  renew  the  surface  of  the  amalgams. 

The  data  and  calculations  for  a  typical  case  follow : 

Composition  of  Amalgam. 

(i)  Pipette  of  amalgam  No.  3  =  121.543 
(2)  Pipette  of  amalgam  No.  3  =  106.845 

Amalgam  No.  3  =     14.698 

(i)  Tube  +  mercury  =  112.26 

(2)  Tube  -|-  mercury  =     69.32 


Weight  of  mercury  =     42.94 

Weight  of  amalgam  No.  3  =     14.70 


Total  weight  of  diluted  amalgam  ■=     sy.6^ 
This  diluted  amalgam  was  called  No.  4. 

Zinc  Dissolved  in  Ammonia  during  Mixing. 

Reading. 

Ferrocyanide  in  burette  (i)  46.25 
Ferrocyanide  in  burette  (2)  46.30 

Ferrocyanide  used  0.05 

Needed  for  end-point  0.0 1 

Total  zinc  dissolved  0.04  X  0.003=0.00012  gram. 

14.70  grams  of  amalgam  containing  0.909  per  cent  of  zinc,  or  0.013  gram 
of  zinc,  were  used ;  0.00012  gram  zinc  is  almost  exactly  o.i  per  cent  of  total. 
Therefore,  the  concentration  ratio  calculated  from  the  weights  of  amalgam 
and  mercury  must  be  multiplied  by  i.ooi  to  correct  for  zinc  dissolved. 


32  ENERGY   CHANGES   INVOLVED   IN   DILUTION    OF  AMALGAMS. 

The  "  parent "  amalgam,  0.91  per  cent,  had  density  13.465,  at  20.00°  C. 
The  new  diluted  amalgam,  11:|  X  0.91  per  cent,  had  density  13.527. 

Then  follows  the  calculation  of  the  concentration  ratio  of  the  two  amal- 
gams, No.  3  and  No.  4 : 


St8Xlfi><'-°°'  =  3-^°«='''^t°-5^'^«- 


In  the  same  way  the  concentration  ratios  of  other  diluted  amalgams  made 
from  No.  3  was  calculated.  These  are  recorded  in  the  following  table. 
The  few  necessary  corrections  for  weights  are  included  without  comment, 
and  the  factors  correcting  for  dissolved  zinc  are  given  without  details. 

Concentration  Ratios  of  Zinc  Amalgams.    Preliminary  Series  {Cell  I). 


No.  of 
amalgam. 

Name  of 
"parent" 
amalgam. 

Weight  of 
"parent" 
amalgam. 

Weight  of 

pure 
mercury. 

Ratio 

of 

densities. 

Factor 
correcting 

for 

dissolved 

zinc. 

Approx. 

per  cent 

zinc  in 

amalgam. 

log 

Cn 

•{ 

4 
5 
6 

Metallic  V» 
zinc,    j 

No.  3 
No.  3 
No.  5 

1.116 
14.698 

7.114 

34.486 

120.98 
42.94 

105.96 

107.24 

13.465 
13.527 
13.465 

1.001 

1.0014 

1.0015 

Fer  cent. 
0.909 

0.232 
0.057 
0.014 

0.00000 
0.59198 

1.19951 

1.81435 

13.540 
13.540 

13.543 

Having  been  thus  prepared,  the  four  amalgams.  No.  3,  No.  4,  No.  5,  and 
No.  6,  were  admitted  into  the  four  cups  of  the  cell  with  all  precautions,  and 
the  potentials  were  measured  under  the  following  conditions : 

Temperature  of  thermostat  (corrected)  23.09°  C.  =  296.17°  abs. 

Temperature  of  i-volt  cell  =1  21°  ;  its  potential  was  therefore  0.9925. 

The  formula  for  the  calculation  of  v  will  be 

_8^i6X_XX2.3026^,      ^ 


2  X  96580 


Xlog 


Log   -^for  the  pair  of  amalgams  No.  4  and  No.  6  is  found  by  subtracting 
log   £8-  from  log  -^  ;  because  -£2.  .^  -£l  =  ^. 

^4  ^6  ^6  ^4  ^« 


"Of  this  zinc  0.006  gram   was   dissolved  in   ammonia   during  the   amalgamation. 
Hence  the  weight  of  zinc  dissolved  in  the  mercury  was  i.iio  or  0.909  per  cent. 


MEASUREMENTS   WITH   ZINC   AMALGAMS. 


33 


Potentials  of  Zinc  Amalgams.    Preliminary  Series  (Cell  I). 


Pair 
meas- 
ured. 

log 

Cn 
Cm 

V  observed 

as  a 

fraction 

of  X 

ir  corrected 
for 
errors  of 
potentio- 
meter. 

IT  in 
interna- 
tional volts. 

IT  calculated 
for^  = 
23.09OC. 

Difference 
IT  calc.  — 
IT  obs. 

a 

3-4 

0.59198 

0.016265 

0.016267 

0.016115 

0.01738 

+  0.001265 

b 

4-5 

0.60753 

0.017685 

0.017664 

0.01753 

0.017835 

+  0.000305 

c 

5-6 

0.61484 

0.018295 

0.018267 

0.01813 

0.01805 

-0.00008 

d 

3-5 

1.19951 

0.033885 

0.033885 

0.03363 

0.03521 

+  0.00158 

e 

3-6 

1.81435 

0.05212 

0.052123 

0.06173 

0.05326 

+  0.00153 

t 

4-6 

1.22237 

0.035915 

0.035901 

0.03563 

0.03588 

+  0.00024 

The  sum  of  the  first  three  potential  differences  must  equal  the  fifth ;  other- 
wise a  cyclic  system  furnishing  work  in  violation  of  the  laws  of  energy  would 
be  conceivable.  As  a  matter  of  fact,  their  sum  is  0.051775  instead  of  0.05173, 
the  sum  of  (a)  and  (b)  is  0.033645  instead  of  0.03363 ;  the  sum  of  (b)  and 
(c)  is  0.03566  instead  of  0.03563.  From  an  analysis  of  these  figures  it  is 
clear  that  the  values  recorded  in  the  first  three  cases  are  all  too  high;  the 
error  is  more  than  o.ooooi  volt  in  every  instance. 

Some  constant  defect,  either  in  the  potentiometer  or  in  the  method  of 
using  it,  is  indicated ;  but  as  this  was  the  first  time  that  formal  measurements 
were  made  with  the  instrument,  these  errors  may  be  excused  if  they  do  not 
occur  again,  and  the  results  may  be  acceptable  so  far  as  they  agree  with 
the  others.  That  both  these  conditions  were  satisfied  will  be  evident  on 
examination  of  the  rest  of  the  work. 

The  measurements  of  other  similar  cells  were  made  with  even  greater  care, 
and  are  recorded  below : 

Concentration  Ratios  of  Zinc  Amalgams.    Second  Series  {Cell  II). 


No.  of 
amal- 
gam. 

"Parent" 
amalgam. 

Weight  of 
"  parent " 
amalgam. 

Weight  of 

pure 
mercury. 

Ratio 

of 

densities. 

Factor 
correcting 

for 

dissolved 

zinc. 

log 

Cg 

Cn 

1 
2 

7 

8 

Zinc. 

No.  1 

No.  1 
No.  2 

*1.1665 
27.020 

21.530 

11.818 

128.89 
133.10 

22.667 

99.99 

13.467 
13.533 
13.467 

1.0025 
1.0005 
1.003 

0.00375 
0.77546 

0.31504 

1.75236 

13.509 
13.533 

13.543 

*In  amalgamating  0.005  gram  of  zinc  was  dissolved  by  ammonia;  hence  the  amalgam 
contained  1.1615  grams  of  zinc,  or  08932  per  cent. 


34 


ENERGY   CHANGES   INVOLVED   IN   DILUTION   OF  AMALGAMS. 


Potentials  of  Zinc  Amalgams.    Second  Series  {Cell  II). 
Temperature  of  thermostat  (corrected)  =  23.01°  =  296.09°  abs. 
Temperature  of  i-volt  cell  20°  ;  electromotive  force  =:  0.9924. 


Pair 
meas- 
ured. 

log: 

Cn 
Cm 

w  observed 

as  a 

fraction 

of  X. 

V  corrected 
for 
errors  of 
potentio- 
meter. 

TTin 
interna- 
tional volts. 

w  calculated 
for<o  = 
23.01  oc. 

Difference 
ircalc— TTobs. 

a 

b 
c 
d 
e 

f 

1-7 
1-2 
1-8 
7-2 
7-8 
2-8 

0.31129 
0.77171 
1 . 74861 
0.46042 
1.48782 
0.97690 

0.00838 

0.02140 

0.050165 

0.01306 

0.04182 

0.028805 

0.008344 

0.021405 

0.050182 

0.01305 

0.041838 

0.028784 

0.00828 
0.02124 
0.04980 
0.01295 
0.04152 
0.028565 

0.009135 

0.02265 

0.05132 

0.013515 

0.042185 

0.02867 

0.000855 

0.00141 

0.00152 

0.000565 

0.000665 

0.00105 

Sum  of  (a)  and  (d)  and  (0=0.049795  ;  (c)  =0.04980. 
Sum  of  (a)  and  (f)  =0.02123  ;     (b)  =0.02124. 

Sum  of  (d)  and  (f)  =0.041515  ;  (e)  =0.04152. 

These  agreements  between  sums  of  several  potential  differences,  and  the 
observed  values  of  the  totals  are  eminently  satisfactory.  In  the  rest  of  the 
final  experiments,  the  checks  obtained  were  uniformly  as  good  as  these; 
therefore,  after  this  measurements  made  merely  as  a  test  of  the  accuracy  of 
others  will  in  general  not  be  included  in  the  tables  of  results. 

The  electromotive  forces  observed  are  constant  throughout  the  day  if  the 
temperature  of  the  cell  remains  unchanged.  After  forty-eight  hours,  during 
which  time  the  supply  of  hydrogen  had  been  discontinued  and  the  thermostat 
had  cooled  down,  cell  II,  when  warmed  up  to  its  previous  temperature,  read 
as  follows: 


No. 

New  value 
observed. 

Old  value 
observed. 

1-2 

1-7 
2-8 
7-2 

0.021415 
0.00839 
0.02888 
0.01807 

0.02140 
0.00838 
0.028805 
0.01806 

All  the  potential  differences  had  increased,  by  an  amount  bearing  a  direct 
relationship  to  the  dilution  of  the  amalgam.  The  causes  of  the  variation 
were  probably  the  diffusion  of  oxygen  from  the  air  into  the  cell,  or  changes 
of  concentration  in  various  parts  of  the  electrolyte  due  to  evaporation  and 
condensation  on  the  upper  part  of  the  cell.  The  differences  are  not  very 
great,  however ;  and  it  is  safe  to  conclude  that  the  earlier  values  are  correct. 

Let  us  now  attempt  to  generalize  the  results  so  far  obtained :  In  all  but 
one  case  the  calculated  potential  exceeds  the  observed ;  the  difference  be- 
tween the  two,  which  from  now  on  we  will  call  Dtt,  is  the  greatest  when  a 


CALCULATION   OF   PRELIMINARY   RESULTS   WITH   ZINC.  35 

concentrated  amalgam  is  compared  with  a  weak  amalgam,  as  in  cell  I  d; 
and  least  when  two  weak  amalgams  are  involved,  as  in  cell  II  /;  in  one 
case  of  the  latter  kind,  I  c,  the  sign  of  the  Dir  has  actually  been  reversed. 

To  exhibit  the  results  graphically,  the  following  plan  might  be  adopted: 
Consider  an  imaginary  series  of  cells,  all  having  for  one  electrode  a  standard 
amalgam,  A^ ,  containing  i  gram  atom  of  zinc  in  the  volume  Fg ,  and  for  the 
other  electrode  different  amalgams  formed  by  diluting  a  given  volume  of  ^3 
to  the  new  volumes  Vn,  Vw,  Vn"  •  •  •  Plot  the  magnitudes  of  V  as  abscissae 
and  the  potentials  of  the  corresponding  cells  as  ordinates;  two  curves,  one 
for  observed  and  the  other  for  calculated  potentials,  result.  The  distance 
they  intercept  on  any  ordinate  measures  Dir  for  the  cell  which  is  defined  by 
the  position  of  that  ordinate. 

Plotted  within  a  reasonable  compass,  these  curves  will  not  be  sensitive 
enough  to  exhibit  fully  the  accuracy  of  the  work,  since  some  of  our  poten- 
tials are  known  to  i  part  in  5,000.  If,  however,  the  common  logarithm  of 
the  concentration  ratio  is  plotted  as  the  abscissa  and  Dtt  as  the  ordinate, 
a  very  compact  and  sensitive  curve  can  be  drawn  (figure  6). 

Amalgam  No.  3,  the  strongest  used  in  the  work,  is  taken  as  the  standard, 
and  all  the  others  referred  to  it.  As  a  matter  of  fact  No.  3  was  never 
actually  compared  with  No.  i,  but  the  calculated  concentration  difference 
was  so  slight  that  the  point  ( i )  can  be  interpolated  without  danger ;  its  ab- 
scissa is  0.00375  ;  and  then  its  ordinate  will  be  0.0000 1.  The  measurements  on 
amalgams  derived  from  No.  i  start  at  that  point  as  from  an  independent 
origin.     In  this  way  all  the  data  so  far  obtained  are  made  comparable. 

The  use  of  this  curve  is  now  easily  extended  to  predict  Dtt  for  any  cell 
containing  two  amalgams,  Am  and  ^n  ,  of  known  concentration. 

Let  iTj  =  potential  calculated  for  cell  A^.-^Am- 
TTg  =  potential  calculated  for  cell  A^^An. 
TTg  =  potential  calculated  for  cell  Am  -^An. 
Then 

TTi  —  DiTi  =  potential  observed  for  cell  A^  -^Am  • 
TTg  —  Dttz  =  potential  observed  for  cell  A^  ->An> 
TTg  —  Z^TTg  =  potential  observed  for  cell  Am  -^  An  . 
Now  TTi  +  TTg  =  TTr,  as  proved  before. 

Also  (tti  —  DiTi)  +  (TTg  —  Dir^)  =X^2  —  -^^2)  for  the  same  reason. 
Therefore,  Dir^  -f-  Dv^  =  Dvz  and  Dtt^  =  Dir^  —  Dttj^  . 


36 


ENERGY   CHANGES   INVOLVED   IN   DILUTION   OF   AMALGAMS. 


Hence  it  is  unnecessary  to  calculate  the  values  tt^  and  ttj  at  all ;  it  is  enough 
to  find  the  logarithm  of  the  concentration  ratio  of  each  amalgam  in  terms 
of  A^  correct  to  o.oi,  to  observe  the  two  ordinates  corresponding  to  these 
logarithms,  and  to  subtract  the  smaller  from  the  greater.  The  difference  is 
Drr^ .  the  desired  quantity. 

1.7 


1.6 


1.4 


I.Z 


0^ 


0.6 


OA 


0.E 


X 

e ■* 

5              9 

8 

k' 

/ 

/ 

4- 

/ 

/ 

/ 

/ 

/ 

M 

0  log  2  log  4-  logs  log  16  log  32  log  64. 

Fig.  6. — Preliminary  Results  with  Zinc  Amalgams. 

Deviations  from  the  theoretical  potential  are  plotted  in  millivolts  as  ordinates; 
logarithms  of  the  concentration-ratios  as  abscissae.  The  most  concentrated  amalgam 
at  the  origin  contained  about  0.9  per  cent  of  zinc.  The  downward  curve  at  the  right 
is  due  to  oxidation. 

Since  Dtt^  +  Dv^  =  Dtt^  we  can  predict  D-rr^  if  Dir^  and  Dir^  are  known. 
This  method  will  be  used  again  and  again  to  get  the  total  ordinate  for  amal- 
gams which  were  not  directly  compared  with  A^.     Of  course  some  risk  of 


CALCULATION    OF    PRELIMINARY   RESULTS    WITH    ZINC.  37 

cumulative  error  is  involved,  but  the  shape  of  the  curve  in  its  different  por- 
tions— the  most  important  question — can  not  be  seriously  altered,  and  the 
percentage  error  can  never  be  increased. 

It  was  now  thought  desirable  to  find  a  point  on  the  curve  between  (5) 
and  (8).     Therefore,  a  new  amalgam.  No.  9,  was  made. 

Weight  amalgam  No.  2  =  18.775 

Weight  mercury  r=  77.90 

Factor  for  Zn  dissolved  =     1.002 

Approximate  per  cent  of  Zn  in  No.  9  =    0.029 

log  -^  =  0.77546 
log -fs- 0.71241+0.77546=  1.48787. 


IT  (2-9)  observed  =  0.02088;  corrected  for  errors  in  potentiometer, 
0.02090 ;  reduced  to  international  volts  0.02074. 

TT  (2-9)  calculated  =  0.020895  ;  Dtr  for  (2-9)  =  0.000155. 

Probable  value  for  Dir  (3-9)  is  the  sum  Dir  (2-9)  +  Dir  (1-2)  and 
D.  (3-1). 

Dtt  (3-9)  =  0.000155  +  0.00141  +  o.ooooi  =  0.001575. 

Point  (9)  fits  the  curve  quite  closely. 

The  curve  as  it  now  stands  predicts  that  the  potential  between  two  amal- 
gams containing  less  than  four-hundredths  of  one  per  cent  of  zinc  will  be 
greater  than  that  required  by  the  osmotic  formula ;  also  that  this  effect  will 
increase  as  infinite  dilution  is  approached.  The  latter  consideration  points 
to  experimental  error  rather  than  faulty  assumptions  in  the  formula,  since 
infinite  dilution  usually  minimizes  disturbing  secondary  effects.  Oxidation, 
the  worst  foe  of  workers  in  this  field,  was  suspected ;  calculation  showed  that 
the  absorption  of  0.00003  gram  of  oxygen  by  each  of  the  dilute  amalgams, 
No.  4,  No.  9,  No.  6,  and  No.  8,  would  account  for  the  falling  off  of  the  curve. 
It  is  quite  possible  that  this  quantity  of  the  gas  may  have  been  absorbed  on 
the  glass  surfaces  used,  or  contained  in  the  hydrogen  bubbled  through  the 
amalgams,  all  our  precautions  notwithstanding.  An  amalgam  so  concen- 
trated as  No.  3  can  not  have  been  injured  in  this  way;  therefore,  if  weighed 
portions  of  it  were  diluted  inside  the  cell  with  mercury  free  from  air,  the 
values  of  Dir  thus  determined  would  be  free  from  error.  Now,  the  risk  of 
losing  minute  drops  of  amalgam  from  the  pipette  tips  would  make  it  inex- 
pedient to  weigh  out  less  than  10  grams  in  each  determination.  It  is  incon- 
venient and  wasteful  to  dilute  such  portions  one  hundred,  fifty,  or  even  ten 
times ;  there  are  also  serious  obstacles  to  the  thorough  mixing  of  such  a  com- 


38  ENERGY   CHANGES   INVOLVED   IN   DILUTION   OF  AMALGAMS. 

bination  without  a  stirrer.  Could  it  be  possible  to  construct  the  last  half  of 
the  true  curve  for  Dir  by  convenient  dilutions  of  the  various  weak  amalgams 
inside  the  cell? 

To  solve  this  problem,  imagine  a  series  of  cells  where  the  concentration 
ratio  is  always  equal  to  an  arbitrary  number — 2,  for  instance.  The  first 
cell  contains  two  concentrated  amalgams,  C^  and  C^ ,  while  in  succeeding 


cells  the  ratio  is  expressed  in  the  general  form where  w  is  a  number  that 

m 
can  be  increased  at  pleasure.  At  the  beginning  of  the  curve  a  comparatively 
small  increment  of  m  will  produce  a  measurable  change  in  the  Dir  of  the 
cell.  But  far  along  on  the  curve,  m  may  be  varied  considerably — several 
per  cent  perhaps — while  Div  remains  sensibly  constant.  Therefore,  if  this 
method  of  diluting  amalgams  is  used,  the  true  concentration  of  amalgam 
Ci  need  not  be  certainly  known  within  i  or  2  per  cent;  the  ratio  alone  is 
needed  exactly  when  the  dilution  of  the  parent  amalgam  is  already  great. 
Some  preliminary  trials  of  this  method  were  now  made.  Pure  mercury 
was  drawn  into  a  pipette  similar  to  those  used  for  amalgams,  and  sealed  up 
without  efforts  to  exclude  air.  The  cell  was  set  up  and  freed  from  air  as 
usual,  and  a  known  portion  of  the  very  dilute  amalgam  No.  8  run  in.  The 
pipette  was  weighed  before  and  after  on  a  large  balance  reading  at  least  to 
milligrams.  The  rapid  succession  of  weighings  made  the  use  of  a  counter- 
poise unnecessary.  Then  a  known  weight  of  mercury  was  run  into  the 
same  compartment  of  the  cell.  The  pipettes  were  tapped  before  removal 
from  the  cell  to  dislodge  loose  drops  from  the  capillaries.  These  were  long 
enough  to  project  into  the  body  of  the  cell,  but  they  did  not  touch  the  electro- 
lyte. Under  these  circumstances  the  loss  in  weight  of  the  pipette  measures 
the  quantity  of  substance  introduced.  Two  dilutions  by  this  method  resulted 
in  the  amalgams  No.  10  and  No.  11,  for  which  the  concentration  ratio  was 
computed  and  the  electrical  measurements  made.  The  densities  of  No.  8 
and  No.  10  are  practically  identical.  There  is  no  titration  correction,  of 
course. 

Quantitative  Data, 
NO.  10. 

Weight  of  amalgam  No.  8,  18.740 
Weight  of  mercury,  '^7'AA'^ 

36.182 


c^        36.182    ,       Cf. 


FURTHER    MEASUREMENTS   WITH    ZINC   AMALGAMS. 
NO.  11. 

Weight  of  amalgam  No.  8,    9.845 
Weight  of  mercury,  11.407 

21.252 

C^  2I.2S2     ,         ^8  o 

V'  =  ~^^^'  ^""^  f  =  0-33418. 


39 


Potential  of  Zinc  Amalgams.    Preliminary  Trial  of  Dilute  Solution. 
n  of  1-volt  cell.  0.9928 :  t  of  thermostat  =  23.08°  C. 


Pair 
ob- 
served. 

n  observed 
fraction  of 
1-volt  cell. 

n  corrected 
fraction  of 
1-volt  cell. 

n  In 

international 

volts. 

JT  calculated. 

2)rr. 

8-10 
8-11 

0.00846 
0.00983 

0.008425 
0 . 00980 

0.00836 
0.009725 

0.008325 
0.009805 

0.000025 
0.00008 

These  results  seem  to  prove  that  Dir  should  be  a  positive  quantity,  even 
when  both  the  amalgams  introduced  are  extremely  dilute.     Since,  however, 

log    ^   is  very  nearly  equal  to  log  ^,  the  marked  difference  in  values  for 

Dir  indicates  experimental  error ;  more  care  must  be  exercised  in  this  process. 

The  only  imaginable  sources  of  error  seemed  to  be  loss  of  material  in 
transferring,  and  failure  to  mix  the  mercury  and  amalgam  thoroughly. 

The  first  difficulty  was  obviated  by  the  use  of  a  capillary  half  a  millimeter 
in  diameter  and  somewhat  tapered  at  its  very  end.  The  shaking  of  the  cell 
was  a  tedious  process,  since  the  glass  gridiron  establishing  a  connection  with 
the  hydrogen  generator  allowed  but  little  play.  After  fifteen  seconds  the 
observed  potential  was  always  equal,  within  a  few  units  in  the  fifth  place,  to 
the  limit  approached  on  long-continued  agitation.  This  limit  was  recorded 
as  the  true  reading  for  the  cell. 

As  might  have  been  expected,  the  first  reading  was  too  high  whenever  the 
mercury  was  run  in  on  top  of  the  amalgam,  and  too  low  in  the  reverse  case. 

A  new  amalgam,  No.  12,  very  nearly  equal  in  concentration  to  No.  5,  was 
now  prepared.  From  it  No.  13,  No.  14,  No.  17,  and  No.  18  were  made  by 
dilution  in  the  cell  as  described  above.  Various  peculiarities  in  the  results 
were  noted,  but  could  not  at  first  be  explained.  Finally  oxidation  was  de- 
tected inside  pipette  No.  12,  and  careful  examination  revealed  a  very  small 
hole,  where  the  upper  tube  had  been  sealed  off.  Experiment  showed  that 
two  different  portions  of  this  amalgam  gave  a  considerable  potential  against 
each  other.  The  remainder  of  No.  12  was  thrown  away,  and  all  results 
obtained  by  its  use  rejected. 


40  ENERGY   CHANGES   INVOLVED   IN   DILUTION   OF  AMALGAMS. 

We  now  resolved  to  conduct  a  series  of  final  measurements,  repeating  all 
those  where  amalgams  more  dilute  than  No.  2  were  concerned,  with  ex- 
treme precautions  against  error.  To  exclude  the  last  trace  of  air  from  the 
process,  the  purest  mercury  was  redistilled  directly  into  a  pipette  as  follows : 
The  condenser  tube  of  the  all-glass  apparatus  previously  described  was  fused 
to  the  inlet  of  the  pipette,  as  it  lay  in  a  horizontal  position.  The  capillary 
tip  was  cut  off  below  the  stopcock,  and  in  its  place  was  fused  the  tube  lead- 
ing to  the  vacuum  pump.  The  distillation  was  conducted  as  usual  in  a 
stream  of  hydrogen  until  300  grams  of  mercury  had  collected  in  the  hemi- 
sphere below  the  inlet  and  outlet  tubes.  Then  the  stopcock  was  closed,  and 
the  system  filled  with  hydrogen.  The  inlet  tube  was  now  fused  off  into  a 
hook  as  usual.  No  important  amount  of  oxygen  could  have  been  present  in 
the  mercury  or  its  atmosphere.  The  vacuum  connection  was  now  cut  off 
and  the  capillary  tip  fused  on  in  its  place.  The  next  problem  was  to  replace 
all  the  air  in  the  outlet  tube  with  mercury.  It  will  not  suffice  to  hold  the 
pipette  upright  and  open  the  stopcock,  since  the  mercury  will  run  down  into 
the  capillary  without  filling  the  intervening  section  of  larger  tubing.  The 
elasticity  of  the  confined  body  of  gas  will  allow  mercury  to  spirt  out  at  every 
jar,  and  will  make  accurate  weighing  impossible.  Therefore,  a  one-hole 
rubber  stopper  receiving  the  outlet  tube  of  the  pipette  was  fitted  into  a  heavy 
test-tube  side-necked  for  a  vacuum  connection  and  a  hydrogen  supply.  When 
all  the  air  present  had  been  replaced  by  hydrogen  the  pressure  was  slightly 
diminished  and  the  tip  of  the  pipette  raised  somewhat  above  the  bulb;  a 
column  of  mercury  still  clung  in  the  tube  connecting  the  stopcock  to  the 
bulb,  and  on  opening  the  stopcock  the  mercury  slowly  rose  into  the  outlet 
tube  and  filled  it  completely.  On  detaching  the  test-tube  and  stopper  the 
pipette  containing  pure  mercury  free  from  oxygen  was  ready  for  use.  With 
this  pure  mercury  was  accomplished  the  dilution  of  amalgams  No.  2,  No.  22, 
and  No.  9  inside  the  cell,  as  follows : 

The  Dilution  of  Amalgam  No.  2. — Quantitative  Data. 
NO.  19. 

Weight  amalgam  No.  2    7732  Ratio  of  densities    13:533 

Weight  mercury  i3-9o5  i3-54i 


0.44825. 


2] 

[.717 

^19 

21.717 
7-732 

X 

13-533. 
13-541' 

^19 

FURTHER   MEASUREMENTS   WITH   ZINC  AMALGAMS. 


41 


NO.  20. 

Weight  amalgam  No.  2    8.631 
Weight  mercury  19.017 

28.248 


Ratio  of  densities 


^3-533 
13-542 


c^   ^28.248   13-533 
c^^        8.631  ^   13.542 

NO.  21. 

Weight  amalgam  No.  2    6.690 
Weight  mercury  12.236 


log7^  =  o-5i467- 


Ratio  of  densities 


13-533 
13-542 


18.026 


18.926 
13533 


6.690  ^  13542 


log-^  =0.45133. 


Potentials  of  Zinc  Amalgams.    Fourth  Series;  Dilute  Amalgams. 
n  Of  1-volt  cell  =  0.9926;  *  of  thermostat  =  23.10O  C. 


Pair 
ob- 
served. 

ir  observed 
fraction  of 
1-volt  cell. 

n  corrected 
fraction  of 
1-volt  cell. 

ir  in 

international 

volts. 

ir  calculated. 

Difference 

Dtt  — 

2-19 
2-20 
2-21 

0.013085 

0.01505 

0.01317 

0.013076 
0.015027 
0.013161 

0.1298- 

0.01491 

0.01306 

0.01316 
0.01511 
0.01325 

0.00018  + 

0.00020 

0.00019 

Here  might  have  been  inserted  the  check  measurements  with  standard 
amalgam,  which  were  just  the  same. 

The  next  portion  of  the  curve  to  be  investigated  lay  beyond  the  point  (5). 
Amalgam  No.  5  was  so  nearly  used  up  that  a  new  amalgam,  No.  22,  had  to 
be  prepared  and  bottled  in  the  original  apparatus. 

Weight  amalgam  No.  i    10.50      Correction  factor  for  Zn    1.0016 


157.54      Ratio  of  densities 


Weight  mercury 

166.04 
Its  concentration  in  terms  of  No.  i, 

c^       168.04^^13.466^  ,      c^  ^ 

Concentration  referred  to  No.  3  log  ^   =  1.20637. 

Cm 

IT  (1-22)  observed  0.03402 

TT  (1-22)  corrected  0.033996 

IT  (1-22)  international  volts  0.03374 

TT  1-22  (calculated)  0.03530 

Dtt  =  0.00156 

Total  ordinate,  0.00156  +  o.ooooi  =  0.00157 


13464 
13-540 


42 


ENERGY   CHANGES   INVOLVED   IN   DILUTION    OF  AMALGAMS. 


When  3-5  was  measured  Dtt  was  0.00158  for  almost  exactly  a  correspond- 
ing dilution.  This  indicates  that  the  oxidation  effect  in  the  bottling  process 
is  very  nearly  constant. 

Returning  to  the  question  of  dilution  of  amalgam  22  inside  the  cell,  we 
have: 

Quantitative  Data. 
NO.  23. 

Weight  amalgam  No.  22  12.606 
Weight  mercury  13463 


Ratio  of  densities 


13-542 
13-544 


26.069 

c^  _  26.069   13542.   g^  -QtT.An 
c^  -  12.606  X  13.544  '  ^""^c..  -  °-3i547. 


:3-544 

NO.  24 

Weight  amalgam  No.  22  11.473 
Weight  mercury  12.259 


Ratio  of  densities    i3v54_2 
13-544 


23.732 
c        23712       13:542 .  io^£«  =  0.31559. 

^n         11.473  ^13544'  ^''^^^i  ^   ^^^ 

Potentials  of  Zinc  Amalgams.    Fifth  Series;  Very  Dilute  Amalgams. 

w  of  1-volt  cell  =  0.9926 ;  t  =  23.09°  C. 


Pair 
ob- 
served. 

IT  observed 
fraction  of 
1-volt  cell. 

w  corrected 
fraction  of 
1-volt  cell. 

n  in 

International 

volts. 

n  calculated. 

Difference 

JDir. 

22-23 
22-24 

0.009325 
0.00933 

0.009285 
0.00929 

0.009215 
0.00922 

0.00926 
0.009265 

0.000046 
0.000045 

This  was  one  of  the  most  pleasing  measurements  in  the  research ;  before 
the  potentials  were  calculated,  the  accidental  agreement  of  these  two  observa- 
tions occasioned  surprise.  When  the  calculations  were  finished,  it  was  seen 
that  the  predicted  values  also  were  very  close  together ;  the  slight  difference 
between  them  was  of  the  expected  size  and  in  the  proper  direction. 

The  Dilution  of  Amalgam  No.  g  Inside  the  Cell. — Quantitative  Data. 


NO.  16. 
Weight  amalgam  No.  9  12.424 
Weight  mercury  14-835 


Ratio  of  densities 


13-543 
13.544 


27.261 


Z^^-T^''^-^"- 


FINAL   MEASUREMENTS   WITH   ZINC   AMALGAMS. 


43 


NO.  16. 


Weight  amalgam  No.  9  13.101 
Weight  mercury  15.846 

28.997 


Ratio  of  densities      ^^t7^ 
13-544 


c^         28.947       I '^.'54'^    ,        ^o 


Potentials  of  Zinc  Amalgams. — Final  Series;  Very  Dilute  Amalgams. 

ir  of  l-volt  cell  =  0.9925;  t  =  23.09O  C. 


Pair 
ob- 
served. 

ir  observed 
fraction  of 
l-volt  cell. 

It  corrected 
fraction  of 
l-volt  cell. 

IT  in 

International 

volts. 

w  calculated. 

Difference. 

9-15 
9-16 

0.01005 
0.01013 

0.01006 
0.01014 

0.00998 
0.01006 

0.010015 
0.01010 

0.000035 
0.00004 

These  results,  of  great  consistency  and  trustworthiness,  make  possible  the 
construction  of  the  true  curve  for  Die  beyond  point  2.  For  this  purpose  it 
is  convenient  to  start  at  point  2,  which  may  be  assumed  for  the  moment  as 
correctly  placed ;  its  abscissa  is  0.077546,  and  its  ordinate,  referred  to  No.  3 
by  interpolation,  is  0.00 141  -|-  0.0000 1  or  0.00142. 


Amalgam. 

Total  abscissa  ^ 

Total  ordinate  Dir^  +  Dir^ 

19 
20 
21 

0.77546  +  0.44825  =  1.22371 
0.77546  +  0.51467  =  1.29013 
0.77540  +  0.45133  =  1.22679 

0.00142  +  0.00018+   =  0.00160  + 
0.00142  +  0.00020       =  0.00162 
0.00142  +  0.00019       =  0.00161 

The  curve  is  now  extended  from  point  2  through  points  19,  20,  and  21 ; 
the  ordinate  (log  ^=  1.20637),  representing  nearly  enough  the  true  con- 
centration of  amalgam  No.  22  intersects  it  at  the  point  22 ;  the  value  of  the 
ordinate  is  thus  fixed  as  0.00160.  Starting  again  from  this  point,  the  curve 
may  be  extended  to  amalgams  23  and  24. 


Amalgam. 

Total  abscissa  — 

Cn 

Total  ordinate  Dn^  +  Drr^ 

23 
24 

1.20627  +  0.31547  =  1.52184 
1.20637  +  0.31559  =  1.52196 

0.00160  +  0.000045  =  0.001645 
0.00160  +  0.000045  =  0.001645 

44  ENERGY    CHANGES   INVOLVED   IN   DILUTION   OF  AMALGAMS. 

In  like  manner  the  value  of  the  ordinate  (log  ^  =  1.48787)  is  fixed  as 

0.00164,  and  the  curve  extended  to  the  still  greater  dilution  of  amalgams 
15  and  16,  made  from  amalgam  9. 


Amalgam. 

Total  abscissa  -^ 

Cn 

Total  ordinate  D»r^  +  I>ir^ 

15 
16 

1.48787  +  0.34125  =  1.83912 
1,48787  +  0.84427  =  1.83214 

0.00164  +  0.000035  =  0.001675 
0.00164  +  0.00004    =  0.00168 

On  plotting  these  values  (figure  7),  the  improvement  due  to  the  rigid 
exclusion  of  oxidation  is  manifest. 

The  close  approach  of  the  "  oxidation  curve "  to  the  true  curve  in  the 
region  of  point  2  shows  that  amalgam  No.  2  v^ras  not  measurably  affected 
by  oxidation;  this  effect  became  manifest  only  v^rith  very  dilute  amalgams; 
it  was  obviously  due  to  the  oxygen  absorbed  during  some  part  of  the  compli- 
cated manipulation  involved  in  the  earlier  experiments. 

Lack  of  time  prevented  the  investigation  of  the  extremely  dilute  amalgams 
beyond  points  15  and  16.  It  seems  safe  to  conclude,  however,  that  the 
observed  potentials  will  continue  to  approach  their  calculated  values  still 
more  closely  as  the  dilution  is  increased,  for  the  curve  is  evidently  becoming 
more  and  more  nearly  horizontal  as  the  dilution  proceeds — that  is  to  say, 
is  approaching  more  and  more  nearly  to  the  requirements  of  the  gas  law. 
It  is  to  be  noted  that  even  amalgams  15  and  16  are  very  dilute,  containing 
only  about  0.014  per  cent  of  zinc  by  weight.  This  matter  will  be  discussed 
further  when  the  results  with  cadmium  have  been  given. 

In  concluding  this  portion  of  the  work,  it  is  worth  while  to  point  out  that 
the  success  of  the  measurements  depended  wholly  upon  the  chemical  side 
of  the  investigation,  namely,  upon  the  purification  of  the  materials,  and 
especially  upon  the  rigorous  exclusion  of  oxidation.  The  physical  measure- 
ments of  course  demanded  great  care,  but  they  involved  nothing  new.  On 
the  other  hand,  the  effect  of  the  few  hundredths  of  a  milligram  of  oxygen 
would  have  wholly  vitiated  the  results  if  this  oxygen  had  not  been  wholly 
excluded ;  and  the  detection  and  elimination  of  this  cause  of  error  caused 
the  chief  labor  of  the  research  and  determines  its  value. 

INFLUENCE  OF  THE  CONCENTRATION  OF  THE  ELECTROLYTE. 

The   electrolyte   used   in   the   original   measurement   of    Nos.    1-22   was 

analyzed  by  titration  with  ferrocyanide  solution.     Its  concentration  was  very 

nearly  one-tenth  molal.     A  new  electrolyte  was  made  up  from  chemically 

pure  zinc  sulphate,  ten  times  as  strong  as  the  above,  and  this  was  freed 


FINAL  RESULTS   WITH   ZINC   AMALGAMS. 


45 


t.7 
1.6 

1.4 

i.2 

1.0 

0.8 
0.6 
0.4- 
0.2 


lOgZ  log  4  top  log  16  log  32  log  64 

Fig.  7. — Final  Results  with   Zinc  Amalgams. 

Deviations  from  the  theoretical  potential  are  plotted  in  millivolts  as  ordinates, 
logarithms  of  the  concentration-ratios  as  abscissae.  The  most  concentrated  amalgam 
at  the  origin  contained  about  0.9  per  cent  of  zinc.  The  dotted  curve  is  a  repetition 
of  figure  6 ;  the  continuous  curve  represents  the  better  results  not  vitiated  by  oxidation. 

from  air  as  before.  With  this  new  electrolyte  measurements  of  the  cell 
1-22  were  repeated,  with  the  result  tt  ^  0.03401,  instead  of  0.03402  as  before. 
These  values  are  practically  identical ;  hence  the  conclusion  of  Richards  and 
Lewis  *"  that  the  potential  of  these  cells  is  independent  of  the  concentration 
of  the  electrolyte  is  confirmed.  There  is  every  reason,  from  a  theoretical 
point  of  view,  for  the  acceptance  of  this  conclusion. 


jja^ 

^^ 

•Ts 

/ 

^ 

**•*» 

- 

/ 

/ 

/ 

/ 

Proc.  Am.  Acad.,  34,  93  (1898). 


46 


ENERGY   CHANGES   INVOLVED   IN   DILUTION   OF  AMALGAMS. 


THE  POTENTIAL  BETWEEN  CADMIUM  AMALGAMS. 

The  study  of  cadmium  was  now  taken  up,  in  the  same  general  manner  as 
that  just  described.  Four  amalgams  were  made  from  the  first  sample  of 
pure  electrolyzed  cadmium,  and  bottled  up  in  pipettes  exactly  as  in  the  case 
of  zinc. 

The  very  dilute  amalgams,  5,  6,  7,  and  8  were  made  inside  the  cells  by 
dilution  with  distilled  mercury  in  hydrogen. 

Concentration  Ratios  of  Cadmium  Amalgams. 


No.  of 
amal- 
gam. 

"Parent" 
amalgam. 

Weight  of 
"  parent " 
amalgam. 

Weight  of 

pure 
mercury. 

Ratio 

of 

densities. 

Factor 
correcting 

for 

dissolved 

Cd. 

Cm 

log,o  - 

1 
2 

8 

4 
9 
6 

6 

7 
8 

Cadmium. 
No.  1. 

No.  1. 

No.  3. 

Cadmium. 

No.  1. 

No.  2. 

No.  3. 

No.  3. 

"4.530 
24.17 

8.949 

35.29 
1.361 
12.226 

12.113 

15.205 

20.526 

148.88 
74.08 

126.79 

94.13 

44.525 

12.762 

11.599 

15.246 

59.818 

is! 372 

1.0007 
1.0025 
1.001 

1.000 
1.000 

1.000 
1.000 

0.60509 
1.17359 
1.73812 

0.30759 
0.89616 
1.47501 
1.76599 

13.593 
13.372 
13.584 
13.534 
13.542 

isisil 

13.458 
13.503 

13.523 
13.534 

13.540 
13.534 

13.542 

From  these  amalgams  two  quadruple  cells  were  made  up,  and  their  electro- 
motive forces  measured  with  all  possible  care. 

The  first  cell  contained  amalgams  i  and  2  as  well  as  5  and  6.  Its  tem- 
perature was  23.03°.     The  potential  of  the  i-volt  cell  was  0.9926  volt. 

The  sum  of  (1-6),  (5-2),  and  (2-6)  is  0.026875  ;  the  direct  measurement  of 
(1-6)  gives  0.02687;  other  similar  checks  are  equally  satisfactory;  hence 
the  potentiometer  readings  are  still  reliable. 


"This  value  is  corrected  for  the  small  amount  of  cadmium  dissolved  by  ammonia 
during  amalgamation.    The  amalgam  contained  2.9553  per  cent  of  cadmium. 


MEASUREMENTS    WITH    CADMIUM    AMALGAMS. 

Potentials  of  Cadmium  Amalgams.    First  Series. 


47 


Pair 

IT  observed 

IT  corrected 

n  in 

Cm 

tr  calculated 
for  to. 

DifTfiTPripp 

meas- 

as a 

fraction 

international 

logio  — 

ured. 

fraction  of  X. 

of  X. 

volts. 

c„ 

If  obs. 

1-5 

0.009505 

0.009472 

0.009405 

0.30759 

0.00903 

-0.000375 

1-3 

0.018428 

0.018405 

0.01827 

0.60509 

0.01776 

-0.00051 

1-6 

0.027098 

0.027067 

0.02687 

0.89616 

0.02630 

-0.00057 

2-6 

0.008690 

0.008664 

0.00860 

0.20107 

0.00854 

-0.00006 

5-2 

0.008052 

0.008935 

0.00887 

0.29750 

0.00873 

-0.00014 

5-6 

0.017615 

0.017597 

0.01747 

0.58857 

0.01727 

-0.00020 

The  second  cell  contained  amalgams  No.  2,  No.  3 ;  also  No.  7  and  No.  8, 
made  by  the  dilution  of  No.  3  inside  the  cell  to  about  one-half  and  one-quarter 
its  original  concentration. 

Its  temperature  was  23.03°  C.  =  296.11°,  and  the  potential  of  the  Helm- 
holtz  cell  was  X  =  0.9929. 

Potentials  of  Cadmium  Amalgams.    Second  Series. 


Pair 
ob- 
served. 

w  observed 

as  a 

fraction. 

IT  corrected 

fraction 

of  X. 

w  in 

international 

volts. 

•o-e^ 

n  calculated 
for  to- 

Difference 
v  calc.  — 
jTobs. 

3-8 
3-7 
2-3 

7-8 

0.017580 
0.008955 
0.016915 
0.008657 

0.017562 
0.008935 
0.016906 
0.008631 

0.017437 
0.008873 
0.016785 
0.008570 

0.59240 
0.30142 
0.56850 
0.29098 

0.017387 
0.008846 
0.016685 
0.008540 

-0.00005 
-0.00003 
-0.00010 
-0.00003 

Calculated  from  3-8  and  3-7,  the  value  of  Dir  for  7-8  is  —  0.00002,  while 
from  the  direct  reading  the  value  is  — 0.00003. 

No  matter  how  satisfactory  a  set  of  readings  appears,  it  should  be  checked 
by  a  determination  in  duplicate.  A  fresh  portion  of  cadmium  was  therefore 
made  Jby  electrolysis  and  converted  into  amalgam  No.  9,  designed  to  have 
as  nearly  as  possible  the  same  concentration  as  No.  i. 

Weight  of  cadmium 1.361 

Weight  of  mercury 44-527 

Cadmium  dissolved  in  ammonia 0.0084 

Percentage  content  of  Cd  No.  9,  calculated, 2.949 

Percentage  content  of  Cd  No.  i,  calculated 2.953 

Density  of  amalgam 9  =  I347i 

From  No.  9  two  amalgams  were  made  by  dilution  inside  the  cell  as  usual. 


48 


ENERGY   CHANGES   INVOLVED   IN   DILUTION    OF  AMALGAMS. 


NO.  10. 

Weight  amalgam  No.  9  11.730 
Weight  mercury  18.077 

29.807 

c^  __  29.807      13.372 
^10  ~  11-730'^  13478 


Ratio  of  densities 


;  log -^  =  0.40159. 

t-IA 


13-372 
13-478 


NO.  11. 

Weight  amalgam  No.  9  1 1.5 16 
Weight  mercury  64.08 


Ratio  of  densities 


13-520 


_  75-596 


X 


75-596 
13-372 


;log^    =  0.81242. 


^11      II.5I6     13.520 

Potentials  of  Cadmium  Amalgams.    Third  Series. 


/  =  23.00° 


X  —  o 


Pair 
ob- 
served. 

ir  observed 

asa 
fraction  of  X. 

w  as  a  cor- 
rected frac- 
tion of  X. 

n  in 

international 

volts. 

log 

ir  calculated 
forte 

Difference 
»  calc.  — 
IT  obs. 

9-10 
9-11 
9-1 

0.01230 
0.24585 
0.00002 

0.012302 
0.024578 
0.00002 

0.012215 

0.02440 

0.00002 

0.40159 
0.81242 
0.00088 

0.011785 
0.023845 

-0.00043 
—  0.000555 

The  curve  for  Dir  in  cadmium  amalgam  cells  can  now  be  constructed  on 
the  same  principles  employed  in  the  case  of  zinc.  The  two  starting  points 
are  so  nearly  identical  that  no  interpolation  is  necessary.  The  summary 
follows. 

Deviations  of  Cadmium  Amalgam  Cells. 


Amalgram 
No. 

Total  abscissa  ^ 

Total  ordinate  Dir„+D»n, 

1 

0.00000 

±  0.00000 

2 

0.60509 

-  0.00051 

3 

1.17359 

-  0.00061 

544 

1.73812 

—  0.000675 

5 

0.30759 

—  0.000375 

6 

0.60509  +  0.29107  =  0.89616 

-  0.00057 

7 

1.17359  +  0.30142  =  1.47501 

-0.00061-0.00003  =  -  0.00064 

8 

1.17359  +  0.59240  =  1.76599 

-0.00061-0.00005  =  -  0.00066 

9 

-  0.00088 

±  0.00000 

10 

0.40159 

-  0.00043 

11 

0.81242 

-  0.000555 

••Interpolated  from  measurements  at  30.00°  and  at  15.20*  by  use  of  absolute  temper- 
ature measurements. 


RESULTS   WITH    CADMIUM   AMALGAMS. 


49 


All  these  points  lie  upon  a  very  satisfactory  curve  except  point  4.  It  will 
be  remembered  that  this  amalgam  was  prepared  outside  the  cell,  as  were 
Nos.  I,  2,  and  3.  The  result  shows  that  clearly  amalgam  4  was  dilute 
enough  to  begin  to  show  the  effect  of  oxidation,  like  that  found  in  the  case 
of  zinc.  On  the  other  hand,  oxidation  has  evidently  not  caused  an  appre- 
ciable error  in  the  ordinate  3;  hence  points  (7)  and  (8),  based  upon  point 
(3),  are  right  also.    The  curve  is  plotted  in  figure  8. 

Attention  is  called  to  the  fact  that  this  curve  of  potentials  is  very  similar 
in  form  to  that  of  zinc,  except  that  the  sign  of  its  curvature  is  exactly  oppo- 
site.    This  point  will  be  discussed  later. 


0.2 


0.4 


0.6 


as 


,5 
< 

>slO 

2 

^4 

""""          ^ 

'~^ 

log  Z  l0|4 


logs 


log  16  log  32       log  64 


Fig.  8. — Results  with  Cadmium  Amalgams. 

Deviations  from  the  theoretical  potential  are  plotted  as  ordinates;  logarithms  of 
the  concentration-ratios  as  abscissae.  The  most  concentrated  amalgams  at  the  origin 
contained  2.95  per  cent  of  cadmium. 


THE  TEMPERATURE  COEFFICIENT  OF  AMALGAM  CELLS. 

Three  pairs  of  cadmium  amalgams  were  investigated  with  great  care  at 
30°,  at  15°,  and  0°.  The  warm  thermostat  (described  above)  maintained 
its  temperature  within  one-hundredth  of  a  degree.  The  intermediate  bath 
had  a  cold-water  coil  more  than  sufficient  to  compensate  for  the  warming 
effect  of  the  surroundings;  the  adjustment  of  temperature  was  accom- 
plished by  an  incandescent  lamp  with  the  usual  electric  cut-off.  The  lowest 
temperature  was  attained  in  a  large  zinc  trough  surrounded  by  cotton  wool 
and  placed  inside  a  wooden  box ;  clear  ice,  finely  divided  and  nearly  covered 
with  distilled  water,  was  used  to  maintain  the  temperature  constant  at  0°  C. 

All  temperatures  were  read  upon  the  Reichsanstalt  thermometer  already 
described ;  corrections  were  made  for  the  zero  point  in  melting  ice,  for  the 


so 


ENERGY   CHANGES   INVOLVED   IN   DILUTION   OF  AMALGAMS. 


known  error  of  the  scale,  and  for  the  exposed  thread.  Ample  time  was 
allowed  for  the  cell  to  reach  the  temperature  of  the  bath.  The  measurements 
follow : 

Temperature  CoeMcient  of  Cadmium  Amalgam  Cells. 


Pair 
observed. 

IT  observed 
as  fraction 

of  1-volt 
cell 

at  80.00°. 

»  In 
inter- 
national 

volts 
at  30.00°. 

n  obseryed 
as  fraction 

of  1-volt 
cell 

at  16.20°. 

n  in 
inter- 
national 

volts 
at  15.20°. 

w  observed 
as  fraction 

of  1-volt 
cell 

at  0.00°. 

ir  in 
inter- 
national 

volts 
at  0.00°. 

r  2-4 

0.034465 

0.034204 

0.032775 

0.032545 

0.031050 

0.080826 

I    . 

1-4 

0.053291 

0.052910 

0.050668 

0.050332 

1-3 

0.036193 

0.035900 

0.034393 

0.034130 

r  2-4 

0.03447 

0.034209 

II    ■ 

1-4 
[    1-8 

0.053295 
0.036189 

0.052914 
0.035896 



The  multiple  cell  after  measurement  at  zero  was  returned  to  the  warm 
thermostat,  and  fifteen  minutes  later  it  gave  almost  exactly  its  original  read- 
ings (see  series  II).  The  results  at  o°  for  combinations  1-3  and  1-4 
are  not  given  in  the  table,  because  at  that  temperature  they  showed  an  ab- 
normally low  potential,  evidently  due  to  a  partial  freezing  of  amalgam  I; 
this  is  consistent  with  the  observations  of  Korp  and  Bottger."  This  fact 
does  not,  of  course,  interfere  with  their  use  at  a  higher  temperature. 

It  becomes  now  a  matter  of  great  interest  to  compare  this  change  of  poten- 
tial with  the  requirements  of  the  gas  law,  by  comparing  the  temperature 
coefficient  with  the  temperature-pressure  coefficient  of  a  perfect  gas  over 
the  same  range  of  temperature. 

The  following  table  gives  the  temperature  coefficients  referred  to  the 
observed  potentials  at  zero : 

2-4,  from  30.00°  to  15.20**. 

Jtt  0.001659 


TT^J/ 


14.80  X  0.030826 


2-4,  from  15.20°  to  0.00°. 


TT.J/ 


1-4,  from  30°  to  15.20* 


—  O.OO1719 

""  15.20  X  0.030826 


0.002578  X  288.20 


7r„J/  ""  14.80  X  273.08  X  0.050332 

1-3,  from  30°  to  15.20°. 

Jtt 0.00177  X  288.20 

14.80  X  273.08  X  0.034130 
Average 


rr^J/ 


=  0.00364 


=  0.00367 


=  0.003655 


=  0.00366 


0.00366  + 


"Zeit.  Anorg.  Chem.,  25,  59  (1900). 


TEMPERATURE   COEFFICIENTS   AND   HEATS   OF  DILUTION.  5 1 

The  agreement  is  surprisingly  good;  within  the  limit  of  accuracy  of  the 
measurement  the  increase  of  the  potential  with  increase  of  temperature  is 
identical  with  the  increase  of  pressure  of  a  perfect  gas.     A  strong  presump- 

tion  in  favor  of  the  constancy  of  ^yat  all  temperatures  is  established  by 
these  measurements. 

Time  did  not  permit  a  careful  study  of  the  temperature  coefficient  of 
pairs  of  zinc  amalgams,  but  enough  was  done  to  show  that  the  agreement 
was  almost  as  good  in  this  case  also.  This  matter  will  be  discussed  pres- 
ently from  another  point  of  view. 

THE  MEASUREMENT  OF  THE  HEAT  OF  DILUTION  OF  THE  AMALGAMS. 

The  next  important  step  in  the  experimental  work  was  to  determine 
directly  the  heat  of  dilution,  in  order  to  apply  rigorously  not  only  the  equa- 
tion of  Helmholtz, 

but  also  the  equation  of  Cady  and  of  Lewis, 

and  thus  to  throw  light  on  the  cause  of  the  deviations  noted  in  the  curves 
discussed  in  the  previous  sections. 

The  great  consistency  and  accuracy  of  the  preceding  electrical  measure- 
ments makes  it  highly  desirable  that  the  heat  of  dilution,  which  in  this  case 
is  the  heat  of  reaction  of  the  system  under  investigation,  should  be  deter- 
mined with  great  precision.  In  order  to  show  the  grade  of  accuracy  needed, 
attention  is  called  to  the  fact  that  each  hundred  thousandth  of  a  volt  in  the 
potential  of  a  concentration  cell  corresponds  to  the  development  of  two  joules 
during  the  transport  of  a  gram  atom.  Consider  now  a  gram  atom  of  zinc 
contained  in  7  kg.  of  amalgam  3  in  the  act  of  dilution  with  an  equal  volume 
of  mercury.  The  heat  capacity  of  the  reacting  mixture  will  not  be  far  from 
2,000  mayers ; "  hence  two  joules  will  produce  in  it  a  temperature  change  of 
one-thousandth  of  a  degree.  If  the  thermometer  can  be  read  as  accurately 
as  this,  the  accuracy  reached  in  the  work  on  potentials  will  be  maintained. 
The  same  dilution  of  a  gram  atom  of  cadmium  in  cadmium  amalgam  No.  I 
will  involve  a  heat  capacity  only  about  half  as  great;  here,  therefore,  the 
thermometer  will  be  read  twice  as  accurately  as  the  potentiometer.  If  the 
amalgam  resulting  from  either  of  the  above  reactions  is  diluted  with  its  own 


'A  mayer  is  the  heat  capacity  raised  1°  C.  by  a  joule. 


52  ENERGY   CHANGES   INVOLVED   IN   DILUTION    OF  AMALGAMS. 

volume  of  mercury,  the  heat  developed  by  the  reaction  is  distributed  over  a 
heat  capacity  double  that  noted  above.  Then  the  thermometer  must  be  read 
twice  as  accurately  as  before  estimated,  in  order  to  compensate  for  this  fact. 

Extending  this  train  of  reasoning,  it  is  evident  that  excessive  refinement 
in  temperature  measurement  would  be  required  to  obtain  a  good  experi- 
mental value  for  the  heat  of  reaction  of  more  dilute  amalgams,  where  the 
heat  capacity  per  gram  molecule  of  zinc  is  enormous.  Limitations  in  time 
made  it  necessary  to  confine  our  attention  to  concentrated  amalgams.  In  all 
probability  the  generalizations  established  for  these  cases  will  apply  at  greater 
dilutions  also. 

The  measurement  of  the  heats  of  dilution  presents  considerable  experi- 
mental difficulties.  Practical  considerations  make  it  desirable  to  limit  the 
weight  of  mercury  used  in  one  experiment  to  5  kg. ;  but  the  small  heat 
capacity  of  such  a  mass  and  its  rapid  conduction  of  heat  demand  extraordi- 
nary constancy  in  the  temperature  of  the  surroundings.  Owing  to  the  high 
inertia  of  mercury  and  its  low  heat  capacity,  efficient  stirring  of  the  mixture 
is  likely  to  produce  a  marked  rise  in  temperature;  this  must  be  estimated 
and  the  corresponding  correction  applied.  Moreover,  the  entire  process  must 
be  carried  out  in  an  indifferent  gas,  to  prevent  oxidation,  with  its  attending 
development  of  heat. 

To  meet  these  requirements  a  new  form  of  calorimeter  was  devised.  The 
principle  of  the  divided  vessel  was  suggested  by  the  work  of  Richards  and 
Lamb,"  but  it  is  believed  that  other  features  of  the  apparatus  constitute  a 
new  departure  in  the  study  of  small  heats  of  reaction. 

The  calorimeter  C  is  shown  in  figure  9.  It  was  made  of  flexible  thin 
iron  plate  seamed  together.  The  partition  P  slid  in  deep  grooves,  b  and  b^, 
while  its  lower  edge  was  received  by  a  shallow  trough  of  sheet  iron  cemented 
to  the  bottom  of  the  calorimeter ;  when  P  is  in  this  position  its  top  is  flush 
with  the  rim  of  the  vessel.  A  grease  containing  about  one  part  of  gum 
rubber,  five  of  hard  paraffin,  and  ten  of  soft  paraffin  applied  around  the  edge 
of  the  partition  made  either  side  of  the  vessel  mercury-tight.  When  the 
ebonite  support  R  had  been  attached,  C  was  lowered  into  the  copper  cylin- 
der F,  leaving  an  air  space  0.7  cm.  in  thickness. 

A  weighed  amount  of  pure  mercury  was  now  run  into  one  side  of  C  from 
a  separating  funnel.  Then  the  clockwork  stirring  apparatus  was  lowered 
into  F  and  bolted  rigidly  to  brass  ledges  soldered  to  the  inner  wall  of  F. 
The  mechanism  consisted  merely  of  the  spring,  its  arbor,  and  one  gear,  whose 
shaft  carried  the  paddle  D.  The  latter  now  dipped  into  the  mercury,  but  its 
blades  lay  flat  against  the  partition  P ;  therefore,  when  the  spring  was  wound 
up  the  paddle  could  not  revolve  until  P  was  pulled  out. 


"Richards  and  Lamb,  Proc.  Am.  Acad.,  40,  657  (1905). 


THE   CALORIMETER. 


53 


The  ebonite  cover  to  the  copper  cylinder  F,  pierced  with  suitable  holes, 
was  now  screwed  to  brass  ledges  soldered  to  the  inner  wall  of  the  cylinder, 
2  cm.  below  its  rim.  The  cracks  were  stuffed  with  tissue  paper.  F  was  then 
lowered  into  an  empty  thermostat,  of  capacity  about  80  liters,  and  a  tube 
delivering  a  rapid  stream  of  pure  dry  carbon  dioxide  was  fitted  into  its 
proper  hole  in  the  cover.     The  outlet  for  the  tube  gas  was  exactly  in  the 


Fig.  9. — Portions  of  the  Apparatus  for  Measuring  the  Heat  of  Dilution. 


center  of  the  cover  and  contained  a  wire  attached  to  the  partition  at  H ;  the 
wire  passed  through  a  small  greased  rubber  tube  fitted  with  a  pinchcock, 
while  the  gas  escaped  through  a  sideneck.  When  all  air  was  displaced,  a 
weighed  amount  of  the  amalgam  to  be  diluted  was  run  into  the  empty  half 
of  C  from  a  separating  funnel  filled  with  carbon  dioxide.  A  Beckmann  ther- 
mometer was  then  lowered  into  the  hole,  and  clamped  firmly  in  place,  its 
bulb  half  way  between  the  surface  and  the  bottom  of  the  amalgam.  All 
the  tubes  leading  into  the  calorimeter  were  also  clamped,  after  which  the 
tenth  of  a  liter  of  a  mixture  of  hard  and  soft  paraffin  melting  at  about  45** 
Centigrade  were  poured  upon  the  ebonite  cover.  This,  when  hard,  made  the 
vessel  F  water-tight ;  but  as  an  additional  precaution  a  small  outward  pres- 
sure of  carbon  dioxide  was  always  maintained  by  closing  all  outlets.  The 
thermostat  was  now  filled  well  above  the  top  of  F,  and  regulated  by  a  very 
large  and  sensitive  electric  cut-off.     The  make  and  break  was  in  an  arti- 


54  ENERGY   CHANGES   INVOLVED   IN   DILUTION    OF   AMALGAMS. 

ficial  atmosphere  of  hydrogen,  and  responded  to  a  change  of  one  or  two 
thousandths  of  a  degree.  Needless  to  say,  a  powerful  stirrer  was  used  to 
keep  the  bath  in  rapid  circulation. 

The  thermostat  was  allowed  to  run  all  night  before  a  determination;  in 
the  morning  the  Beckmann  thermometer  was  absolutely  stationary  at  the 
temperature  of  the  bath  outside.  The  partition  P  was  pulled  out  by  means 
of  the  wire  mentioned  above ;  the  paddle,  when  thus  released,  revolved  about 
fifty  times  before  the  spring  ran  down.  The  temperature  change  was  read 
oif  on  the  Beckmann  thermometer  with  careful  tapping  to  avoid  friction  of 
the  thread. 

Unless  mercury  and  amalgam  are  in  perfect  thermal  equilibrium  before 
the  experiment,  the  initial  temperature,  read  from  the  single  thermometer  in 
the  amalgam,  will  not  represent  the  average  temperature  of  the  reacting 
mixture.  Seventeen  hours  at  constant  temperature  on  all  sides  should  in- 
sure this  condition  for  a  comparatively  small  volume  of  a  substance  con- 
ducting heat  so  well  as  mercury.  Blank  runs,  however,  were  made  with  pure 
mercury  to  test  the  truth  of  the  assumption  thus  made.  No  cooling  correc- 
tion, of  course,  was  necessary,  though  five  minutes  were  allowed  for  the 
thermometer  to  become  constant. 

Blank  experiment  i:  Temperature  change  -j-  o.ooi°. 

Blank  experiment  2:  Temperature  change  +  0.006°. 

This  irregularity  was  found  to  be  due  to  uneven  heating  of  the  calorimeter, 
by  radiation  from  the  lamp  used  for  heating  the  thermostat.  This  radiant 
heat  maintained  one-half  the  mercury  at  a  slightly  higher  temperature  than 
the  other,  on  a  cold  night  when  the  lamp  was  in  operation  most  of  the  time. 
On  this  account  an  electric  heating  coil  30  cm.  in  diameter  was  substituted 
for  the  lamp ;  its  plane  was  horizontal,  and  the  vessel  F  was  exactly  in  its 
center.  Uneven  heating  could  not  now  occur,  and  the  following  blank 
experiments  proved  the  change  to  have  accomplished  its  object: 

Blank  experiment  3:  The  thermometer  fell  0.001°,  and  then  rose  to  its 
original  position. 

Blank  experiment  4:  The  thermometer  rose  0.002°. 

The  mean  of  these  trials  indicates  that  a  correction  of  — 0.001°  in  each 
experiment  should  suffice  for  our  purpose.  This  is  to  be  ascribed  to  the  work 
done  by  the  clockwork  stirrer. 

A  zinc  amalgam  (0.9  per  cent)  was  now  made  from  pure  stick  zinc  and 
mercury  purified  with  mercurous  nitrate.  The  manipulation  of  the  two 
determinations  of  the  heat  of  dilution  of  this  amalgam  has  already  been 
described. 


RESULTS   CONCERNING   HEAT   OF   DILUTION. 
Cooling  Effect  on  Diluting  Zinc  Amalgam. 


55 


Weight 
of  mercury. 

Weight 
of  amalgam. 

Temperature 
change. 

I 
II 

Grams. 
2523 
2303 

Gram^. 
2303 
2303 

-0.021 
-0.0225 

In  the  first  case  the  stirrer  probably  ceased  to  revolve  after  a  few  revolu- 
tions ;  in  the  second  case  it  worked  efficiently.  The  mean  fall  of  temperature 
in  this  cooling  effect  is  0.022° ;  corrected  for  the  heat  of  stirring  it  becomes 
0.023°. 

The  total  energy  change  of  dilution  is  equal  to  the  product  of  the  heat 
capacity  and  the  temperature  increment,  0.023°.  The  heat  capacity  is  found 
as  follows : 

Heat  capacity, 
in  mayers. 

2,300  grams  of  mercury 317 

2,300  grams  of  amalgam "  320 

130  grams  of  iron 60 

5  grams  of  grease  and  cement  (estimated) 16 

Thermometer   (estimated)    13 

Total  heat  capacity  720 

Therefore  the  energy-change  was  720  X  —  0.023  =  —  16.6  joules. 

The  2,300  grams  of  amalgam  contained     ^3QQ  X  0.0091  ^^^j^  ^£  ^:^^^ 

054 
Hence  the  total  energy-change  involved  in  the  same  dilution  of  a  gram- 
atom  of  zinc  is : 

—  16.6  X  ^^ =  —  52  joules. 

2300  X  0.0091 

The  further  dilution  of  a  zinc  amalgam  containing  less  than  I  per  cent  of 
zinc  thus  causes  a  very  appreciable  cooling  effect. 

The  cadmium  used  to  make  amalgams  for  the  investigation  of  heats  of 
dilution  was  the  commercial  "  pure  "  article,  but  of  course  its  purity  was  not 
above  suspicion.  Inasmuch  as  the  dilution  of  the  small  amount  of  impurity 
which  it  might  contain  could  not  cause  an  appreciable  heat  effect,  its  use 
was  justifiable  for  these  measurements.  Even  2  per  cent  of  zinc  could  cause 
at  the  most  a  temperature  change  of  only  0.001°. 

"This  value  was  found  in  a  special  series  of  determinations  to  be  described  else- 
where. 


56  ENERGY   CHANGES   INVOLVED   IN   DILUTION   OF  AMALGAMS. 

Absolutely  no  change  of  temperature  was  noted  upon  withdrawing  the 
partition  in  either  of  two  apparently  perfect  experiments  on  the  dilution 
of  this  3  per  cent  cadmium  amalgam.  If  the  clockwork  stirrer  caused  heat 
enough  to  raise  the  temperature  o.ooi°,  the  dilution  of  the  cadmium  amal- 
gam could  not  have  had  a  cooling  effect  on  dilution  of  much  more  than  this. 
Therefore,  it  seems  probable  that  the  total  internal  energy-change  involved 
in  the  dilution  of  a  3  per  cent  cadmium  amalgam  by  pure  mercury  is  neg- 
ligibly small,  not  over  i.o  joule  per  gram  atom;  and  it  is  further  probable 
that  the  dilution  of  cadmium  amalgams  of  lower  concentrations  absorb  even 
less  heat. 

Before  accepting  these  results,  a  determination  on  pure  mercury  and  on 
each  amalgam  was  made  by  another  method.  The  clockwork  was  dispensed 
with,  and  a  second  thermometer  inserted  so  that  one  thermometer  was  im- 
mersed in  each  of  the  liquids  to  be  mixed.  A  hand  stirrer  whose  shaft  was 
incased  in  a  long  glass  tube  projected  into  the  calorimeter.  The  other  feat- 
ures of  the  process  remained  unchanged.  After  a  long  time  at  constant  tem- 
perature the  partition  was  pulled  out  and  hand  stirring  begun.  As  expected, 
the  vertical  motion  of  a  small  circle  of  glass  rod  was  far  less  satisfactory  than 
the  automatic  paddle  which  it  replaced ;  the  rate  of  mixing,  as  inferred  from 
the  movements  of  the  thermometers,  was  slow,  and  the  clumsy  stirring  was 
attended  by  the  evolution  of  much  heat.  The  superposition  of  this  effect 
upon  the  true  heat  of  dilution  gave  rise  to  ill-defined  results.  None  of  these, 
however,  threw  doubt  on  the  measurements  obtained  by  the  first  method ; 
hence  the  extremely  small  heat  effect  in  the  dilution  of  cadmium  amalgams 
was  confirmed. 

It  may  here  be  stated  that  besides  these  calorimetric  experiments,  others 
were  instituted  in  order  to  determine  the  change  of  heat  capacity  of  a  metallic 
system  during  amalgamation."  The  heat  capacity  of  both  zinc  and  cad- 
mium amalgams  were  studied,  and  were  found  to  be  slightly,  but  only 
slightly,  greater  than  some  of  the  heat  capacities  of  the  mercury  and  other 
metal  before  mixing.  The  difference  was  so  slight  that  it  is  safe  to  assume 
that  the  further  dilution  of  either  amalgam  involves  no  appreciable  change 
of  heat  capacity.  Hence  these  experiments  need  not  be  described  in  detail 
here ;  they  will  be  recounted  at  length  in  another  place. 

"Richards,  Henderson  and  Forbes,  Proc.  Am.  Acad.,  41,  8  (1905). 


THE   APPLICATION    OF   THE   EQUATION    OF    HELMHOLTZ.  57 

THE  APPLICATION  OF  THE  EQUATION  OF  HELMHOLTZ. 

According  to  the  equation  of  Helmholtz," 

the  sum  of  the  heat  of  reaction  and  the  product  of  the  absolute  temperature 
and  the  temperature-coefficient  of  the  change  of  free  energy  should  equal 
the  change  of  free  energy  itself. 

In  the  case  of  the  cadmium  cell  it  is  possible  to  prove  the  rigorous  applica- 
tion of  this  equation,  because  all  the  quantities  are  known. 

For  example,  taking  the  cell  2-4  (which  gives  about  the  average  tempera- 
ture coefficient),  we  have 

ttq  =  0.030826  volt 
Att  =  0.001719  volt 
AT  =  15.20° 
7=273.09° 

V  =  2 

F  =  96,580 
U  =  — o.ooi 

Therefore,  for  the  left-hand  number  we  have 

5.95  —  o.ooi  =  5.95  kilojoules 
and  for  the  right-hand  =  5.95  kilojoules 
showing  a  difference  of       .00 

The  difference  between  the  two  members  of  the  equation  is  thus  certainly 
less  than  the  probable  magnitude  of  the  experimental  error.  No  more  satis- 
factory verification  of  this  equation  has  ever  been  offered ;  and  the  case  is  of 
especial  interest  because  of  the  extremely  small  value  of  the  heat  of  reaction. 

The  Helmholtz  equation  can  not  be  supported  in  the  same  way  by  the 
results  with  zinc,  because  lack  of  time  prevented  us  from  determining  its 
temperature-coefficient  with  sufficient  accuracy.  On  the  other  hand,  know- 
ing the  heat  of  dilution  on  doubling  the  volume  of  a  0.91  per  cent  zinc  amal- 
gam to  be  —  0.052  kilojoules  (see  page  55),  the  temperature-coefficient  of  a 
cell  of  this  kind  can  easily  be  calculated  with  the  help  of  the  Helmholtz  equa- 
tion.    Transposed  for  this  purpose  "  the  equation  becomes 

A^  —  1  I  52 

AT~  T'^  2X96,580  X  T 

•"In  this  case     Att   and    ^T  can  be  substituted  for  the  infinitesimals,  as  the  heat 
capacity  does  not  change  on  dilution. 
*"  See  Richards  and  Lewis,  Proc.  Am.  Acad.,  34,  88  (1898). 


58  ENERGY   CHANGES   INVOLVED   IN   DILUTION    OF   AMALGAMS. 

Selecting  the  cell  1-7  (see  page  34)  as  representing  the  dilution  in  question, 
we  have  the  following  data :  tt  =  0.00828,  T  =  273.09°  +  23.01°  =  296.1°  ; 

therefore,  -^  =  0.00002796  and ^\ =,  =  0.00000099.    Hence   -=^ 

2  2  X  9^>5"^  X  -/  iJi 

=  0.00002892.  From  this  it  is  easily  calculated  that  ir  at  0°  is  0.00762  and 
^j.  is  0.00379.  It  is  interesting  to  note  that  through  a  partial  compensa- 
tion of  opposite  effects  this  temperature-coefficient  of  electromotive  force 
should  be  brought  to  within  about  3  per  cent  of  the  temperature-coefficient 
of  pressure-increase  in  a  perfect  gas  (0.00366).  Previous  experiments** 
were  not  accurate  enough  to  detect  any  difference  at  all  between  these 
values.    The  present  values  are  more  trustworthy,  because  the  most  doubtful 

quantity,  the  last  term  above  (  2  v  q6  1^80  X  7^  )  ^^"  hardly  be  in  error  by  an 
amount  which  would  affect  the  result  0.3  per  cent. 

THE  APPLICATION  OF  THE  FORMULA  OF  CADY. 

While  there  is  thus  every  reason  to  believe  that  the  Helmholtz  equation 
applies  with  great  exactness  to  the  phenomena  under  consideration,  the  case 
is  very  different  with  equation  of  Cady, 

Vi  ^F        Vi       v/P 

This  equation  is  now  to  be  considered. 

Selecting  again  similar  cells  for  this  comparison,  we  have  for  the  cadmium 
cell  1-5  from  the  table  on  p.  47. 

^-^  In^  =  +  0.000375  volt 

and  from  p.  56  -^= ''^    „    =  —  0.000005  volt 

^  ^  i>F      2  X  96,580         ^ 

Difference  =  -f  0.00038    volt 

This  difference  corresponds  to  about  forty  times  the  probable  error  of  the 
potential  readings,  and  nearly  eighty  times  the  probable  error  in  the  estimation 
of  the  heat  of  dilution ;  moreover,  the  quantities  are  actually  different  in  sign. 

The  deviation  in  the  case  of  zinc  is  even  more  marked,  although  in  this 
case  the  two  members  of  the  Cady  equation  at  least  have  the  same  sign. 
The  figure  for  the  potential  of  a  cell  made  from  amalgam  3  and  one  only 
half  as  concentrated  are  less  by  0.00085  than  the  theoretical  value  based  on 


Richards  and  Lewis,  Proc.  Am.  Acad.,  34,  94  (1898). 


THE   DEVIATIONS    FROM    THE    FORMULA   OF    CADY.  59 

the  volumes,  and  the  heat  of  dilution  was  found  to  be  — 52  joules  for  an 
amalgam  equally  concentrated.     Hence 

TT  —  ^  in'^-^  =  —  0.00085  volt 

-^  = — 0.00027  volt 

Difference      —  0.00058  volt 

This  value  has  even  a  larger  percentage  accuracy  than  the  one  computed 
for  cadmium,  and  like  that  one  can  not  but  signify  a  real  discrepancy. 

Because  in  neither  case,  then,  the  equation  of  Cady  was  found  to  hold 
exactly  true,  it  is  clear  that  some  modifying  influence  must  be  at  work.  It 
does  not  by  any  means  follow  that  the  effects  depicted  by  Cady's  equation 
do  not  really  represent  part  of  the  influences  producing  electromotive  force ; 
but  clearly  this  equation  does  not  contain  a  complete  or  exact  account  of 
all  these  influences. 


THE  PROBABLE  CAUSES  OF  THE  DEVIATIONS. 

It  becomes  now  a  matter  of  great  interest  to  speculate  concerning  the  prob- 
able cause  of  the  discrepancy ;  for  an  uncomprehended  irregularity  is  always 
suggestive  of  unknown  but  possibly  knowable  effects. 

Many  possible  superposed  effects  have  been  suggested  as  capable  of  modi- 
fying results  of  this  kind.  Of  these  the  most  important  may  be  discussed 
in  general  before  proceeding  to  particulars. 

In  the  first  place,  it  has  been  suggested  that  the  space  occupied  by  the 
dissolved  substance  should  be  taken  into  consideration.  This  was  first  sug- 
gested, perhaps,  by  A.  A.  Noyes,"  when  working  with  Ostwald,  and  has 
received  striking  support  in  the  recent  osmotic  experiments  of  H.  N.  Morse 
already  cited.  The  further  suggestion  of  Noyes,  that  the  volume  of  the 
molecules  of  solvent  also  should  be  subtracted,  is  of  a  more  hypothetical 
nature,  and  seems  to  receive  less  support  from  the  facts. 

Secondly,  the  suggestion  of  compounds  of  solvent  and  solute  (hydrates  in 
aqueous  solution,  or  hydrargyrates  in  mercurial  solutions)  has  been  made  to 
explain  many  phenomena  of  the  two  classes  of  solutions.  Marignac,  de 
Coppet,  and  Riidorff  all  considered  this  possibility  and  inclined  toward  it 
long  ago.  More  recently  H.  C.  Jones  has  revived  the  theory ;  and  Haber's 
recent  extension  of  it  to  mercurial  solutions  has  already  been  discussed. 
There  is  nothing  unreasonable  in  this  idea. 

Thirdly,  it  is  conceivable  that  although  the  amalgam  holds  most  of  its 
dissolved  metal  in  a  monatomic  form,  a  part  remains  polymerized,  or  in  a 


"Noyes,  Zeitschr.  Phys.  Chem.,  5,  53  (1890). 


60  ENERGY   CHANGES   INVOLVED   IN   DILUTION   OF   AMALGAMS. 

hydrargyrate  containing  two  or  more  atoms  of  the  solute  to  the  molecule. 
This  equally  plausible  contingency  simply  postulates  that  a  balanced  reaction 
such  as  2Zn  %,  Zn^  or  2ZnHgn  %  Zn^Hgn-m  +  Hgm  exists  in  the  solution. 
Such  a  reaction  would  of  course  be  pushed  from  right  to  left  by  diluting  the 
amalgam. 

It  has  been  suggested  also  that  changes  of  heat  capacity  should  be  con- 
sidered in  probing  to  the  uttermost  the  equation  of  Cady.  In  the  present 
case,  however,  this  possibly  disturbing  effect  is  eliminated,  for  we  have 
shown  that  the  change  of  heat  capacity  which  takes  place  on  diluting  either 
zinc  or  cadmium  amalgam  is  so  slight  as  to  cause  no  suspicion  that  this  phe- 
nomenon can  have  anything  to  do  with  the  observed  irregularities. 

The  most  probable  disturbing  agencies  having  thus  been  discussed  in 
general,  the  particular  cases  under  consideration  may  be  considered.  As  has 
been  made  clear,  the  amalgams  of  the  two  metals  vary  in  opposite  ways  from 
the  theory,  cells  of  zinc  amalgams  giving  potentials  too  low  and  cells  of 
cadmium  amalgam  giving  potentials  too  high.  The  two  must,  then,  be  con- 
sidered separately ;  and  of  the  two,  cadmium  may  most  conveniently  be  con- 
sidered first,  because  it  presents  the  least  irregularity. 

One  of  the  striking  facts  in  relation  to  cadmium  amalgam  is  the  fact  that 
its  heat  of  dilution  is  so  small  as  to  be  negligible.  Therefore,  the  equation 
of  Helmholtz  reduces  practically  to  the  form 

making  the  thermodynamics  of  the  problem  as  simple  as  possible. 

The  only  irregularity  which  this  cell  of  cadmium  amalgams  manifests  is 
the  following,  namely,  with  all  except  the  most  dilute  amalgams 

irvF  >  RTln  i^ 

Thus  from  the  volume-energy  point  of  view  the  cadmium  acts  like  hydro- 
gen— a  gas  "  more  than  perfect." 

But  in  this  equation  the  left-hand  member  represents  a  statement  of  fact, 
and  R  and  T  are  definite  quantities  whose  product  is  only  very  slightly 
uncertain.  Therefore,  it  seems  probable  that  the  only  remaining  term,  the 
ratio  of  V2  to  v^ ,  is  not  correctly  chosen. 

It  will  be  remembered  that  this  term  was  always  evaluated  on  the  assump- 
tion (i)  that  the  metal  dissolved  in  mercury  is  strictly  monatomic,  (2)  that 
it  forms  no  compound  with  the  solvent,  and  (3)  that  it  obeys  the  laws  of 
perfect  gases  with  exactness.  If  the  first  condition  is  not  satisfied,  the  poten- 
tial will  be  lowered ;  if  the  second  or  the  third  is  violated,  the  reverse  effect 
will  probably  prevail. 


SPECULATIONS   CONCERNING  ATOMIC   VOLUMES.  6l 

In  the  case  of  cadmium  the  observed  potential  is  higher  than  the  calculated 
value;  hence  either  the  second  or  third  (or  both)  disturbing  effects  may  be 
supposed  to  predominate  over  the  first.  It  will  be  seen  that  these  excessive 
values  of  the  potentials  with  great  concentrations  are  precisely  parallel  with 
the  excessive  values  of  osmotic  pressures  in  concentrated  aqueous  solutions, 
observed  especially  by  H.  N.  Morse  and  his  assistants,  in  his  very  important 
researches  on  this  subject.  Here  as  there,  the  simplest  explanation  seems  to 
be  that  a  portion  of  the  total  volume  is  not  effective  as  a  receptacle  for  the  dis- 
solved cadmium;  and  it  becomes  highly  interesting  to  speculate  as  to  the 
magnitude  of  this  useless  space. 

Any  calculation  of  this  kind  must  involve  assumptions  of  some  kind,  and 
it  is  important  that  the  assumptions  should  be  as  reasonable  as  possible.  In 
a  preliminary  trial,  it  may  be  assumed  that  the  useless  space  does  not  vary 
with  the  volume,  and  that  there  is  complete  absence  of  polymerization. 

The  ratio  of  the  values  of  the  useful  space  in  the  two  amalgams  may  be 
derived  at  once  from  the  following  equation : 

when  v^  and  v^  are  the  ideal  or  hypothetical  volumes  of  the  useful  space. 
The  actual  ratio  of  the  volumes  is,  however, 

found  directly  from  the  weight  W^  and  W^  and  the  densities  D^  and  D^ 
of  the  two  masses  of  amalgam  containing  the  same  weight  of  cadmium. 

Now,  calling  the  useless  space  b  and  assuming  it  to  possess  a  constant 
value  (that  is,  assuming  V2  =^  v^  -\-  b  and  v^  =:  v^  -{-  b)  we  have  from  (i) 

^V2  d  VTtF 


vy-^b-  RT 


(3) 


or  from  (2)  and  (3) 

In 


or, 


Hence 


\        ■v.  —  b       /      RT 
\  1  -  anti  In^j,)  =  v,  [^^  -  ant.  In  ^  • 

JT^.-""^'  '"Rt)  (5) 


(  I  —  anti  In  ~d-j-\ 


62 


ENERGY   CHANGES   INVOLVED   IN   DILUTION    OF  AMALGAMS. 


Calculated  thus,  h  in  cell  1-5  is  found  to  be  15.8  milliliters,  in  cell  1-2,  14.4 
milliliters,  in  cell  2-5,  12.7  milliliters,  and  in  cell  3-8,  21  milliliters,  for  an 
amount  of  amalgam  containing  a  gram-atom  of  cadmium.  Owing  to  the 
extreme  dilution,  the  value  for  cell  3-8  has  a  very  great  probable  error  and 
may  be  rejected.  The  average  of  the  others  is  14.3  milliliters,  a  quantity 
very  near  the  gram-atomic  volume  of  cadmium,  13.0.  Thus  if  from  the 
actual  volume  of  the  amalgam  the  space  originally  occupied  by  the  cadmium 
is  subtracted,  the  remaining  volumes  v^  and  Vq  very  nearly  fulfill  the  equation 

RTln  -^  =  TTvF. 

The  following  table  illustrates  this  relation,  and  is  comprehensible  without 
further  comment : 


Designation 
of  cell. 

Potential  of 

ceil  calculated 

from  actual 

volumes. 

Potential  calculated 

from  volumes 

after  subtraction 

of  volume  of  Cd. 

Observed 
potentials. 

1-5 
1-2 
2-5 

0.00903 
0.01776 
0.00873 

0.00933 
0.01821 
0.00888 

0.00940 
0.01827 
0.00887 

Evidently,  while  the  correction  greatly  improves  the  agreement  between 
the  theoretical  and  the  observed  values,  there  is  still  a  slight  discrepancy, 
especially  with  the  stronger  amalgams.  The  "  useless  volume  "  is  in  most 
cases  slightly  larger  than  the  volume  of  the  cadmium.  Does  this  signify 
that  the  cadmium  expands  on  amalgamation,  while  causing  the  mercury 
which  surrounds  it  to  contract  somewhat  more  than  it  expands?  This  is 
conceivable,  although  the  total  effect  on  amalgamating  a  gram-atom  of  cad- 
mium is  a  contraction  of  about  1.3  milliliters,  as  calculated  from  the  densi- 
ties. Or,  on  the  other  hand,  does  some  of  the  mercury,  combining  with  the 
cadmium,  remove  itself  from  the  possibility  of  functioning  as  a  solvent  and 
thus  add  to  the  useless  volume  ?  Yet  another  possibility  also  exists.  It  may 
be,  as  has  been  already  suggested,  that  this  value  of  the  useless  volume  is 
really  nothing  but  an  accidental  balance  between  the  opposing  tendencies — 
that  the  true  value  is  really  considerably  larger,  including  at  least  a  gram- 
atom  of  mercury  in  addition  to  one  of  cadmium,  but  that  the  true  value  does 
not  appear  because  of  the  counterbalancing  presence  of  polymerization.  It 
will  be  seen  that  in  the  case  of  zinc  this  latter  effect  seems  to  be  the  pre- 
dominant one. 

Further  light  could  be  obtained  by  determining  the  osmotic  pressure  of  the 
cadmium  in  solution,  because  this  would  be  dependent  upon  the  sum  of  the 
osmotic  pressures  of  the  various  molecular  species,  instead  of  having  their 
effect  counterbalance.     If  the  deviation  of  this  value  of  the  osmotic  pressure 


THE   PROBABLE   CAUSES    OF   THE   DEVIATIONS.  63 

from  the  theoretical  coincided  with  the  inference  from  deviation  in  the  elec- 
tromotive force,  it  would  be  reasonable  to  suppose  that  both  deviations  were 
due  to  the  same  ultimate  cause,  and  that  this  was  the  only  cause. 

The  only  results  which  seem  to  have  been  obtained  upon  this  matter  are 
those  of  Ramsay  on  the  decrease  of  vapor  pressure  of  mercury  at  260° 
caused  by  the  solution  of  a  metal.  He  found  the  atomic  weight  of  cadmium 
in  three  solutions  containing  0.04,  1.08,  and  1.92  per  cent  of  cadmium  to  be 
100.2,  99.7,  and  103.8,  respectively.  Neglecting  the  first  of  these  results, 
because  the  amalgam  was  then  too  dilute  for  sufficient  percentage  accuracy, 
the  others  give  an  average  atomic  weight  of  101.8  (instead  of  the  true  value 
112.5)  for  cadmium  in  an  amalgam  containing  1.5  per  cent  of  this  metal. 
The  osmotic  pressure  was  therefore  about  10  per  cent  too  great  in  this  1.8 
atomic-normal  solution.  Such  an  excess  is  four  times  as  large  as  that  which 
would  be  caused  by  a  "  useless  space  "  equal  to  the  volume  of  the  dissolved 
cadmium,  for  this  amalgam  is  essentially  like  amalgam  5  of  this  paper,  which 
has  just  been  calculated  to  show  a  "  useless  "  space  of  only  about  2.5  per 
cent  of  the  total  volume. 

In  short,  while  both  Ramsay's  results  and  ours  vary  from  the  simplest 
theory  in  the  same  direction,  they  differ  greatly  in  the  amount  of  variation ; 
and  if  both  are  to  be  trusted,  taken  together  they  point  not  only  to  the  for- 
mation of  hydrargyrates  in  the  amalgam,  but  also  to  polymerization.  Ram- 
say's results,  nevertheless,  need  confirmation  before  they  can  be  accepted 
without  question,  as  they  are  not  very  numerous,  and  vary  considerably 
among  themselves.  Further  treatment  of  the  matter  must  be  postponed  until 
more  knowledge  has  been  obtained  concerning  these  osmotic  pressures.  The 
subject  is  being  studied  further  in  this  laboratory. 

The  case  of  zinc  may  be  reviewed  more  briefly,  although  it  also  presents 
very  interesting  features.  Here,  instead  of  giving  too  high  an  electromotive 
force,  the  zinc  amalgams  give  one  less  than  the  theoretical.  A  part  of  this 
deficiency  is  to  be  ascribed  to  the  thermal  effect  depicted  by  the  formula  of 
Cady ;  but  as  is  shown  on  page  59  this  formula  explains  only  one-third  of  the 
total  deviation.  In  view  of  the  outcome  of  the  preceding  discussion,  it  seems 
necessary  to  refer  the  otherwise  unexplained  deficiency  to  the  polymeriza- 
tion of  a  part  of  the  zinc. 

This  assumption  of  polymerization  is  supported  by  all  the  other  facts 
bearing  upon  the  question.  In  the  first  place,  we  have  found  that  the  dilu- 
tion of  a  I  per  cent  amalgam  absorbs  considerable  heat,  showing  that  the 
same  reaction  which  occurs  on  amalgamating  is  still  occurring — and  the  cool- 
ing part  of  this  reaction  must  be  supposed  to  consist  in  the  disintegration  of 
the  zinc.     However,  this  effect  must  not  be  too  hastily  connected  with  the 


64 


ENERGY    CHANGES   INVOLVED   IN    DILUTION    OF   AMALGAMS. 


Splitting  Up  of  chemical  union  among  the  atoms ;  it  might  also  be  referred  to 
a  less  definite  attraction,  one  similar  to  that  causing  the  Joule-Thomson  effect 
in  gases.  In  mercurial  solutions  this  attraction  would  be  the  difference  be- 
tween two  affinities,  but  for  our  purposes  it  can  be  treated  as  a  single  quan- 
tity. Now,  in  the  free  expansion  of  carbonic  acid  from  ten  atmospheres  to 
normal  pressure,  a  cooling  effect  of  1.4°  C.  occurs;  if  the  molecular  heat 
is  taken  as  40  mayers,  56  joules  are  absorbed  by  each  gram  molecule. 
When  a  gram-atom  of  zinc,  in  the  calorimeter,  expands  from  44  to  20  atmos- 
pheres osmotic  pressure,  without  doing  outside  work,  52  joules  are  absorbed. 
Clearly  it  would  be  possible  to  account  for  the  cooling  effect  alone  without 
assuming  chemical  dissociation. 

In  the  next  place,  Tammann  "*  found  that  zinc  even  in  amalgams  as  weak 
as  0.2  per  cent  lowers  the  freezing  point  of  the  mercury  by  a  deficient  amount, 
not  exceeding  nine-tenths  of  the  theoretical  value — which  indicates  that  the 
normal  fully  dissociated  condition  had  not  been  attained. 

Again,  Ramsay  found  an  atomic  weight  of  dissolved  zinc  even  at  260**, 
which  was  certainly  not  less  than  the  true  value  (the  average  of  three  de- 
terminations was  65.9). 

Finally,  further  evidence  showing  that  zinc  is  more  inclined  to  double  its 
atoms  in  mercurial  solution  than  cadmium  may  be  obtained  by  comparing 
the  volume  changes  occurring  when  a  gram-atom  of  zinc  or  of  cadmium  is 
dissolved  in  varying  amounts  of  mercury.  These  changes  are  easily  found 
from  the  data  given  on  page  14  as  follows : 

(i)  Zinc  Amalgams. 


Amalgam. 

Per  cent  of 

dissolved 

metal. 

Observed 
density. 

Volume  of 

factors  in  cell, 

calculated. 

Volume  of 
products  in 

cell, 
calculated. 

Contraction 

in  cell, 
calculated. 

1 
2 
3 
4 

0.821 
0.733 
0.644 
0.180 

18.472 
13.482 
13.493 
18.580 

593.2 

663.2 

754.2 

2686.9 

591.9 

661.8 

752.7 

2685.8 

1.3 
1.4 
1.5 
1.6 

(2)  Cadmium  Amalgams. 


5 

2.97 

18.870 

284.2 

288.0 

1.2 

4 

2.30 

13.405 

852 . 0 

350.6 

1.4 

2 

0.74 

13.503 

1126.2 

1124.8 

1.4 

3 

0.37 

13.527 

2247.6 

2246.2 

1.4 

Zeit.  Phys.  Chem.,  3,  441  (1889). 


EXTRAPOLATION    TO   INFINITE   DILUTION. 


6s 


The  atomic  volumes  of  zinc  and  cadmium  were  taken  as  respectively  9.5 
and  13.0  in  making  these  calculations. 

Thus  in  both  cases  the  system  suffers  contraction  when  the  amalgamation 
takes  place.  The  striking  point  is  that  zinc  amalgams  continue  to  contract 
when  diluted,  showing  apparently  that  molecular  rearrangement  is  still  in 
progress.  The  contraction  of  cadmium,  however,  does  not  increase  so 
greatly,  a  sign  that  the  monatomic  condition  prevails  more  nearly  in  concen- 
trated amalgams  of  this  metal. 

None  of  these  results  is  accurate  enough  to  form  the  basis  of  exact  quan- 
titative calculation,  but  all  point  in  the  same  direction.  When  more  accu- 
rate measurements  of  the  osmotic  pressure  have  been  made,  further  produc- 
tive speculation  concerning  the  extent  of  this  strongly  indicated  partial 
association  of  zinc  in  concentrated  amalgams  will  be  possible. 

THE  APPLICATION  OF  THE  GAS  LAW  AT   INFINITE  DILUTION. 

It  is  interesting  to  note  that  whatever  may  be  the  cause  of  the  superposed 
effects,  the  sum  total  of  irregularities  in  the  case  of  zinc  and  cadmium  dimin- 
ishes in  each  case  at  about  the  same  rate  as  dilution  proceeds.  The  follow- 
ing table  gives  the  values  of  the  difference  between  the  observed  potentials 
and  those  demanded  by  the  gas  law,  when  various  amalgams  of  zinc  and  cad- 
mium are  compared  with  the  extrapolated  value  for  infinite  dilution.  These 
values  are  taken  from  the  curves  given  on  pages  45  and  49. 


Diflference  between  observed 

potential  of  cells  and  that  calculated 

CJoncentration  In 

from  gas  law. 

gram  atoms 
per  liter. 

Zinc. 

Cadmium. 

Volt. 

Volt. 

[0.00] 

-[0.00000] 

+  [0,00000] 

0.03 

-   0.00002 

+    0.00001 

0.06 

—  0.00004 

+   0.00002 

0.12 

—   0.00009 

+   0.00004 

0.28 

-  0.00019 

+   0.00007 

0.47 

-   0.00041 

+   0.00011 

0.93 

-  0.00084 

+   0.00018 

1.87 

—   0.00168 

+  0.00033 

Evidently  the  doubling  of  the  concentration  in  each  case  produces  a  nearly 
double  amount  of  the  irregularity ;  hence  the  curves  are  very  similar  in  shape. 
The  results  are  advantageously  depicted  together  in  figure  10. 


(£ 


ENERGY   CHANGES   INVOLVED   IN   DILUTION   OF  AMALGAMS. 


This  diagram  illustrates  in  a  striking  manner  the  most  definite  and  per- 
haps the  most  important  outcome  of  the  research,  namely,  the  fact  that  each 


♦0^ 


♦•0.2 


\ 

^^Cd 

/ 

r 

Zn 

• 

/ 

/ 

/ 

'■■ 

•0.2 


•a4 


•0.6 


'0.8 


-1.0 


•1.2 


•1.4 


■1.6 


-1.8 

log  2         log 4  logs  log  16  log  32  log  64       log  128       log  256 

Fig.  id. — ^The  Approach  of  the  Potentials  of  Amalgam  Cells  to  the  Gas  Law. 

Deviations  are  plotted  in  millivolts  as  ordinates;  concentration-ratios  as  abscissae. 
The  most  concentrated  amalgams  contain  each  1.87  gram-atoms  per  liter.  The  dotted 
lines  are  extrapolated. 


CONCLUSION.  67 

amalgam  approaches  the  theoretical  value  required  by  the  gas  law  more  and 
more  closely  as  dilution  proceeds.  The  further  fact  that  one  of  these  series 
of  results  approaches  the  limiting  value  from  below  and  the  other  from 
above  increases  the  probability  that  the  gas  law  holds  perfectly  in  solutions 
of  infinitesimal  concentration.  From  the  lower  side  we  have  approached  the 
ideal  value  within  0.3  per  cent,  from  the  upper  side  within  0.2  per  cent,  and 
have  seen  that  further  dilution  would  undoubtedly  yield  yet  closer  results. 
The  osmotic  pressure  of  zinc  or  cadmium  in  the  most  dilute  amalgams 
investigated  was  about  one  atmosphere;  it  is  interesting  to  note  that  the 
irregularities  in  p  v  existing  here  appear  scarcely  greater  than  those  of 
oxygen  and  hydrogen  gases,  whose  molal  volumes  are  22.39  and  22.44  liters, 
respectively,  under  normal  conditions.  This  outcome  seems  to  be  incon- 
sistent with  the  idea  that  the  hypothetical  bulk  of  the  molecules  of  solvent 
affects  the  osmotic  pressure. 

Without  doubt  the  present  research  thus  gives  the  most  rigid  experimental 
proof  of  the  exactness  of  the  gas  law  in  dilute  mercurial  solutions  ever 
obtained.  Whether  so  close  an  approach  has  ever  been  noted  in  other 
solvents  is  doubtful. 

In  concluding  this  somewhat  lengthy  and  troublesome  investigation,  it  is 
a  pleasure  to  acknowledge  the  important  pecuniary  aid  generously  granted 
by  the  Carnegie  Institution  of  Washington.  This  support  materially  facili- 
tated the  work. 


68  ENERGY   CHANGES   INVOLVED   IN   DILUTION   OF  AMALGAMS. 


SUMMARY. 

The  main  points  of  the  present  research  may  be  summarized  as  follows : 

1.  The  potentials  between  various  liquid  amalgams  were  investigated 
at  23°  C.  Extraordinary  precautions  were  taken  against  experimental  errors, 
and  the  misuse  of  absolute  units.    The  results  are  reliable  within  0.0000 1  volt. 

2.  Zinc  amalgams  gave  potentials  lower  than  those  calculated  from  the 
gas  law;  and  cadmium  amalgams  gave  potentials  higher  than  those  calcu- 
lated from  the  gas  law.  The  regular  and  symmetrical  curves  thus  con- 
structed show  the  close  approach  of  these  deviations  to  zero  as  the  dilution  is 
increased. 

3.  In  the  most  dilute  amalgams  investigated  the  closest  approach  to  the 
gas  law  ever  noted  in  the  study  of  solutions  was  found. 

4.  The  temperature-coefficient  of  the  potential  of  the  cadmium  amalgam 
cell  was  shown  to  be  almost  exactly  identical  with  the  tension  increments  of 
a  perfect  gas,  and  that  of  the  concentrated  zinc  amalgam  cell  about  3  per 
cent  greater. 

5.  The  heats  of  dilution  of  the  amalgams  were  measured  directly  by  a 
new  and  accurate  calorimetric  process,  and  the  results,  taken  in  connection 
with  the  temperature-coefficient  of  the  potential,  afford  a  striking  verification 
of  the  Helmholtz  equation. 

6.  On  the  other  hand,  the  formula  of  Cady  is  found  to  be  inadequate  to 
explain  exactly  the  deviations  from  the  gas  law.  In  no  case  does  the  cor- 
rection indicated  by  this  formula  account  for  more  than  a  small  part  of  the 
deviations  of  potential.  Therefore,  Cady's  equation  is  incomplete.  The 
uncertainty  is  shown  to  consist  probably  in  the  method  of  evaluating  the 
volumes  to  be  used  in  the  calculation. 

7.  The  densities  of  liquid  zinc  and  cadmium  amalgams  were  carefully 
measured,  and  the  extent  of  the  contraction  which  takes  place  on  mixing  was 
computed  in  each  case. 

8.  The  constitution  of  zinc  and  cadmium  amalgams  is  discussed  from 
chemical  and  kinetic  standpoints.  The  irregularities  of  zinc  cells  are  traced 
primarily  to  partial  polymerization,  those  of  cadmium  cells  maiilly  to  abnor- 
mal osmotic  pressures.  The  situation  is  shown  to  be  too  complex  for  the 
complete  quantitative  treatment  of  these  different  tendencies  until  further 
results  upon  osmotic  pressure  have  been  obtained. 

The  Chemical  Laboratory  of  Harvard  College, 
October,  1903,  to  June,  1906. 


r^ 


v'#\'  W'  ''«!'''••>«»•  "''i™''  "«**  ;>■?»':>>»»  «w;,Tsm\\;m\Y  ..y 


W'MMV 


THIS  BOOK  IS  DUE  ON   THE  LAST  DATE 
STAMPED  BELOW 


RENEWED  BOOKS  ARE  SUBJECT  TO  IMMEDIATE 
RECALL 


DEC^    IS91 


RECEIVED 


DEC 


i  i33] 


*Hys  SCI  UBHAfl^ 


WMm 


LIBRARY,  UNIVERSITY  OF  CALIFORNIA,  DAVIS 

Book  Slip-50m-8,'66(G5530s4)458 


Richards,  T.w. 

Energy  changes  involved 
in  the  dilution  of  zinc 
and  caxlmlum  amalgams. 

PHYSICAL 
SCIENCES 
LIBRARy 


cadmium 


3_I175  00657  1783 


